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data-section-name="Neutrosophic-Logic-&-Infographics" data-toggle="tab" href="#neutrosophiclogicinfographics" role="tab" style="border: none;"><span>1</span> Neutrosophic Logic & Infographics</a></li></ul></li></ul></div><div class="divider ds-divider-16" style="margin: 0px;"></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Florentin Smarandache</h3></div><div class="js-work-strip profile--work_container" data-work-id="127519330"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519330/Uncertain_Labeling_Graphs_and_Uncertain_Graph_Classes_with_Survey_for_Various_Uncertain_Sets_"><img alt="Research paper thumbnail of Uncertain Labeling Graphs and Uncertain Graph Classes (with Survey for Various Uncertain Sets)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519330/Uncertain_Labeling_Graphs_and_Uncertain_Graph_Classes_with_Survey_for_Various_Uncertain_Sets_">Uncertain Labeling Graphs and Uncertain Graph Classes (with Survey for Various Uncertain Sets)</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Graph theory, a branch of mathematics, studies the relationships between entities using vertices ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Graph theory, a branch of mathematics, studies the relationships between entities using vertices and edges. Uncertain Graph Theory has emerged within this field to model the uncertainties present in real-world networks. Graph labeling involves assigning labels, typically integers, to the vertices or edges of a graph according to specific rules or constraints. This paper introduces the concept of the Turiyam Neutrosophic Labeling Graph, which extends the traditional graph framework by incorporating four membership values—truth, indeterminacy, falsity, and a liberal state—at each vertex and edge. This approach enables a more nuanced representation of complex relationships. Additionally, we discuss the Single-Valued Pentapartitioned Neutrosophic Labeling Graph.The paper also examines the relationships between these novel graph concepts and other established types of graphs. In the Future Directions section, we propose several new classes of Uncertain Graphs and Labeling Graphs. And the appendix of this paper details the findings from an investigation into set concepts within Uncertain Theory. These set concepts have inspired numerous proposals and studies by various researchers, driven by their applications, mathematical properties, and research interests.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ff6a455ca8cbd806bf13631d7ec55895" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241201,"asset_id":127519330,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241201/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519330"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519330"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519330; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519321"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519321/Uncertain_Automata_and_Uncertain_Graph_Grammar"><img alt="Research paper thumbnail of Uncertain Automata and Uncertain Graph Grammar" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519321/Uncertain_Automata_and_Uncertain_Graph_Grammar">Uncertain Automata and Uncertain Graph Grammar</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Graph theory has been widely studied, resulting in numerous applications across various felds. Am...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Graph theory has been widely studied, resulting in numerous applications across various felds. Among its many topics, Automata and Graph Grammar have emerged as signifcant areas of research. This paper delves into these concepts, emphasizing their adaptation to uncertain frameworks like Fuzzy, Neutrosophic, Vague, Turiyam Neutrosophic, and Plithogenic systems. By integrating uncertainty into traditional graph theoretical models, the paper aims to address ongoing research challenges and expand the scope of these models.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="701d1811b09af01e4fe99ac13fff33de" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241190,"asset_id":127519321,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241190/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519321"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519321"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519321; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519309"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519309/Three_Novel_Approaches_to_Deep_Space_Interstellar_Travel_that_Transcend_the_Limitations_Imposed_by_the_Rocket_Equation"><img alt="Research paper thumbnail of Three Novel Approaches to Deep Space: Interstellar Travel that Transcend the Limitations Imposed by the Rocket Equation" class="work-thumbnail" src="https://attachments.academia-assets.com/121241179/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519309/Three_Novel_Approaches_to_Deep_Space_Interstellar_Travel_that_Transcend_the_Limitations_Imposed_by_the_Rocket_Equation">Three Novel Approaches to Deep Space: Interstellar Travel that Transcend the Limitations Imposed by the Rocket Equation</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In the past decades, there has been growing interest in novel approaches beyond existing technolo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In the past decades, there has been growing interest in novel approaches beyond existing technologies, especially to explore the Deep Space and beyond [1-3]. In this regard, the Tsiolkovsky rocket equation, a cornerstone of astronautics, provides a fundamental relationship between a spacecraft's initial mass, final mass, exhaust velocity, and the change in velocity it can achieve. While this equation has been instrumental in numerous space missions, it also presents inherent limitations that hinder our ability to explore the vast expanse of the universe [1]. One significant limitation of the Tsiolkovsky equation is the requirement for carrying propellant. The more propellant a spacecraft carries, the heavier it becomes, necessitating even more propellant to accelerate that increased mass. This creates a feedback loop that limits the maximum achievable velocity. As a result, long duration missions to distant destinations, such as Mars or beyond, become increasingly challenging and resource-intensive.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0e59448b7524ab2337ce47ad444e6e85" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241179,"asset_id":127519309,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241179/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519309"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519309"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519309; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519294"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519294/Symbolic_HyperPlithogenic_Set"><img alt="Research paper thumbnail of Symbolic HyperPlithogenic Set" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519294/Symbolic_HyperPlithogenic_Set">Symbolic HyperPlithogenic Set</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigate...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structured set defined by symbolic components 𝑃 𝑖 and coefficients 𝑎 𝑖 , enabling flexible algebraic operations under a specified prevalence order. In this paper, we examine concepts including the Symbolic HyperPlithogenic Set and the Symbolic 𝑛-SuperhyperPlithogenic Set.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="35129813d210e04261d65fd731c95a70" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241159,"asset_id":127519294,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241159/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519294"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519294"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519294; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519271"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519271/Survey_of_Planar_and_Outerplanar_Graphs_in_Fuzzy_and_Neutrosophic_Graphs"><img alt="Research paper thumbnail of Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519271/Survey_of_Planar_and_Outerplanar_Graphs_in_Fuzzy_and_Neutrosophic_Graphs">Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">As many readers may know, graph theory is a fundamental branch of mathematics that explores netwo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">As many readers may know, graph theory is a fundamental branch of mathematics that explores networks made up of nodes and edges, focusing on their paths, structures, and properties [196]. A planar graph is one that can be drawn on a plane without any edges intersecting, ensuring planarity. Outerplanar graphs, a subset of planar graphs, have all their vertices located on the boundary of the outer face in their planar embedding. In recent years, outerplanar graphs have been formally defined within the context of fuzzy graphs. To capture uncertain parameters and concepts, various graphs such as fuzzy, neutrosophic, Turiyam, and plithogenic graphs have been studied. In this paper, we investigate planar graphs, outerplanar graphs, apex graphs, and others within the frameworks of neutrosophic graphs, Turiyam Neutrosophic graphs, fuzzy graphs, and plithogenic graphs.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bcc700d388339bf94868255491be7d8b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241129,"asset_id":127519271,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241129/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519271"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519271"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519271; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519233"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519233/Superhypergraph_Neural_Networks_and_Plithogenic_Graph_Neural_Networks_Theoretical_Foundations"><img alt="Research paper thumbnail of Superhypergraph Neural Networks and Plithogenic Graph Neural Networks: Theoretical Foundations" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519233/Superhypergraph_Neural_Networks_and_Plithogenic_Graph_Neural_Networks_Theoretical_Foundations">Superhypergraph Neural Networks and Plithogenic Graph Neural Networks: Theoretical Foundations</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhyp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as Fuzzy Graphs and Neutrosophic Graphs have gained prominence. It is well established that Plithogenic Graphs serve as a generalization of both Fuzzy Graphs and Neutrosophic Graphs. Furthermore, the Fuzzy Graph Neural Network has been proposed and is an active area of research. This paper establishes the theoretical foundation for the development of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, expanding the applicability of neural networks to these advanced graph structures. While mathematical generalizations and proofs are presented, future computational experiments are anticipated.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="869d85180cf3f6077839dc1d698c1e47" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241116,"asset_id":127519233,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241116/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519233"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519233"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519233; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519223"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519223/Some_Types_of_HyperNeutrosophic_Set_7_Type_m_Nonstationary_Subset_valued_and_Complex_Refined"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519223/Some_Types_of_HyperNeutrosophic_Set_7_Type_m_Nonstationary_Subset_valued_and_Complex_Refined">Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundational advancements introduced in [26,39-43]. The Neutrosophic S...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundational advancements introduced in [26,39-43]. The Neutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f070cdbdb10f40386464369eeb11258" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241106,"asset_id":127519223,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241106/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519223"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519223"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519223; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518955"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518955/Some_Types_of_HyperNeutrosophic_Set_6_MultiNeutrosophic_Set_and_Refined_Neutrosophic_Set"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (6): MultiNeutrosophic Set and Refined Neutrosophic Set" class="work-thumbnail" src="https://attachments.academia-assets.com/121240865/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518955/Some_Types_of_HyperNeutrosophic_Set_6_MultiNeutrosophic_Set_and_Refined_Neutrosophic_Set">Some Types of HyperNeutrosophic Set (6): MultiNeutrosophic Set and Refined Neutrosophic Set</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds on the foundational advancements introduced in [22, 29-32]. The Neutrosophic Se...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds on the foundational advancements introduced in [22, 29-32]. The Neutrosophic Set provides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0fc5ab8ff17cb7a5d5088a6ff5453b6f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240865,"asset_id":127518955,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240865/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518955"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518955"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518955; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518945"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518945/Some_Types_of_HyperNeutrosophic_Set_5_Support_Paraconsistent_Faillibilist_and_Others"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others" class="work-thumbnail" src="https://attachments.academia-assets.com/121240854/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518945/Some_Types_of_HyperNeutrosophic_Set_5_Support_Paraconsistent_Faillibilist_and_Others">Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundational advancements introduced in [14, 25-27]. The Neutrosophic ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundational advancements introduced in [14, 25-27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20].</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="511a9198baad9c4ae38088e5255c97a8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240854,"asset_id":127518945,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240854/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518945"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518945"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518945; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518921"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518921/Some_Types_of_HyperNeutrosophic_Set_4_Cubic_Trapozoidal_q_Rung_Orthopair_Overset_Underset_and_Offset"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (4): Cubic, Trapozoidal, q-Rung Orthopair, Overset, Underset, and Offset" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518921/Some_Types_of_HyperNeutrosophic_Set_4_Cubic_Trapozoidal_q_Rung_Orthopair_Overset_Underset_and_Offset">Some Types of HyperNeutrosophic Set (4): Cubic, Trapozoidal, q-Rung Orthopair, Overset, Underset, and Offset</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundational work presented in [38-40]. The Neutrosophic Set provides ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundational work presented in [38-40]. The Neutrosophic Set provides a comprehensive mathematical framework for managing uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set, which are specifically designed to address increasingly complex and multidimensional problems. The formal definitions of these sets are available in [30]. In this paper, we extend the Neutrosophic Cubic Set, Trapezoidal Neutrosophic Set, q-Rung Orthopair Neutrosophic Set, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset using the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set. Furthermore, we briefly examine their properties and potential applications.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="18040d114c59f3b0f3d1c50666716b8e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240838,"asset_id":127518921,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240838/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518921"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518921"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518921; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518901"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518901/Some_Types_of_HyperNeutrosophic_Set_3_Dynamic_Quadripartitioned_Pentapartitioned_Heptapartitioned_m_polar"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, m-polar" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518901/Some_Types_of_HyperNeutrosophic_Set_3_Dynamic_Quadripartitioned_Pentapartitioned_Heptapartitioned_m_polar">Some Types of HyperNeutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, m-polar</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a ro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e522e63b5aa2201ea16d3753aee6e238" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240833,"asset_id":127518901,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240833/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518901"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518901"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518901; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518890"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518890/Some_Types_of_HyperNeutrosophic_Set_2_Complex_Single_Valued_Triangular_Fermatean_and_Linguistic_Sets"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, and Linguistic Sets" class="work-thumbnail" src="https://attachments.academia-assets.com/121240824/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518890/Some_Types_of_HyperNeutrosophic_Set_2_Complex_Single_Valued_Triangular_Fermatean_and_Linguistic_Sets">Some Types of HyperNeutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, and Linguistic Sets</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathe...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathematical framework for managing uncertainty, characterized by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to address more complex and multidimensional challenges. In this study, we extend the Complex Neutrosophic Set, Single-Valued Triangular Neutrosophic Set, Fermatean Neutrosophic Set, and Linguistic Neutrosophic Set within the frameworks of Hyperneutrosophic Sets and SuperHyperneutrosophic Sets. Furthermore, we investigate their mathematical structures and analyze their connections with other set-theoretic concepts.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="512e7aa440a8ce58e7708e435cf8c510" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240824,"asset_id":127518890,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240824/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518890"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518890"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518890; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518857"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518857/Some_Types_of_HyperNeutrosophic_Set_1_Bipolar_Pythagorean_Double_Valued_Interval_Valued_Set"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set" class="work-thumbnail" src="https://attachments.academia-assets.com/121240771/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518857/Some_Types_of_HyperNeutrosophic_Set_1_Bipolar_Pythagorean_Double_Valued_Interval_Valued_Set">Some Types of HyperNeutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by three membership functions: truth (T), indeterminacy (I), and falsity (F). In recent years, extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set have been introduced to address more complex scenarios. This paper proposes new concepts by extending Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets using the frameworks of Hyperneutrosophic and SuperHyperneutrosophic Sets. Additionally, a brief analysis of these extended concepts is presented.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45df8088343b9419a47c58571543e7b4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240771,"asset_id":127518857,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240771/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518857"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518857"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518857; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518840"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518840/Some_Graph_Parameters_for_Superhypertree_width_and_Neutrosophictree_width"><img alt="Research paper thumbnail of Some Graph Parameters for Superhypertree-width and Neutrosophictree-width" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518840/Some_Graph_Parameters_for_Superhypertree_width_and_Neutrosophictree_width">Some Graph Parameters for Superhypertree-width and Neutrosophictree-width</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Graph characteristics are often studied through various parameters, with ongoing research dedicat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Graph characteristics are often studied through various parameters, with ongoing research dedicated to exploring these aspects. Among these, graph width parameters-such as treewidthare particularly important due to their practical applications in algorithms and real-world problems. A hypergraph generalizes traditional graph theory by abstracting and extending its concepts [77]. More recently, the concept of a SuperHyperGraph has been introduced as a further generalization of the hypergraph. Neutrosophic logic [133], a mathematical framework, extends classical and fuzzy logic by allowing the simultaneous consideration of truth, indeterminacy, and falsity within an interval. In this paper, we explore Superhypertree-width, Neutrosophic treewidth, and t-Neutrosophic tree-width.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="170c36d829883e7ed1519f629afda0ad" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240758,"asset_id":127518840,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240758/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518840"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518840"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518840; 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Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518817"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518817/Significado_Neutros%C3%B3fico_Partes_comunes_de_cosas_poco_comunes_y_partes_poco_comunes_de_cosas_comunes"><img alt="Research paper thumbnail of Significado Neutrosófico: Partes comunes de cosas poco comunes y partes poco comunes de cosas comunes" class="work-thumbnail" src="https://attachments.academia-assets.com/121240735/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518817/Significado_Neutros%C3%B3fico_Partes_comunes_de_cosas_poco_comunes_y_partes_poco_comunes_de_cosas_comunes">Significado Neutrosófico: Partes comunes de cosas poco comunes y partes poco comunes de cosas comunes</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificaci...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificación de elementos comunes entre conceptos opuestos y en el análisis de las diferencias entre conceptos semejantes. En este contexto, se estudian las Partes Comunes a Cosas No Comunes, que se manifiestan cuando elementos como <A> y < antiA > comparten aspectos en su intersección, y las Partes No Comunes a Cosas Comunes, donde conceptos iguales como <A> y <B> difieren al exhibir elementos únicos. Este análisis permite comprender mejor la neutralidad e indeterminación representada por < neutA > y < neutB >, situados entre sus respectivos opuestos. La investigación abarca diversas áreas como la Dialéctica, el Yin Yang, y teorías sociales como el Capitalismo y el Socialismo, así como enfoques en Psicoanálisis y Psicología analítica, destacando la Intención paradójica en la comprensión de fenómenos y teorías, desde la Democracia hasta la Terapia cognitivo-conductual y la Terapia psicodinámica.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f8435eb72afc18a13fbed6bcb5e90200" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240735,"asset_id":127518817,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240735/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518817"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518817"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518817; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518796"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518796/Remark_on_Falaco_Soliton_as_a_Tunneling_Mechanism_in_a_Navier_Stokes_Universe"><img alt="Research paper thumbnail of Remark on Falaco Soliton as a Tunneling Mechanism in a Navier-Stokes Universe" class="work-thumbnail" src="https://attachments.academia-assets.com/121240719/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518796/Remark_on_Falaco_Soliton_as_a_Tunneling_Mechanism_in_a_Navier_Stokes_Universe">Remark on Falaco Soliton as a Tunneling Mechanism in a Navier-Stokes Universe</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is a follow up to our previous article [1] suggesting that it is possible to find tunn...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is a follow up to our previous article [1] suggesting that it is possible to find tunneling time solutions for Schrodinger equation considering quasicrystalline as interstellar matter, by virtue of quasicrystalline potential. The paper also discusses the mapping of these equations to Riccati equations, a class of nonlinear differential equations. This mapping can provide insights into the behavior of the Navier-Stokes equations and may lead to new methods for solving them. The Navier-Stokes equations, a set of nonlinear partial differential equations, are fundamental in fluid mechanics. They describe the motion of viscous fluids. In three dimensions, these equations are particularly complex and often leading to turbulence. The paper also discusses shortly on Falaco soliton as a tunneling mechanism in a Navier-Stokes Universe, which is quite able to fill the gap of realistic mechanism of quantum tunneling which is missing in standard Wave Mechanics. Further investigations are advised.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e842a232cdbe7195def29edc70ec4538" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240719,"asset_id":127518796,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240719/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518796"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518796"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518796; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518761"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518761/Reconsideration_of_Neutrosophic_Social_Science_and_Neutrosophic_Phenomenology_with_Non_classical_logic"><img alt="Research paper thumbnail of Reconsideration of Neutrosophic Social Science and Neutrosophic Phenomenology with Non-classical logic" class="work-thumbnail" src="https://attachments.academia-assets.com/121240698/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518761/Reconsideration_of_Neutrosophic_Social_Science_and_Neutrosophic_Phenomenology_with_Non_classical_logic">Reconsideration of Neutrosophic Social Science and Neutrosophic Phenomenology with Non-classical logic</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering sign...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision-making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective p roblem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in fields such as social s ciences. By incorporating Neutrosophic Sets, we aim to improve their suitability for programming and mathematical analysis, providing advanced methods to tackle complex, multi-dimensional problems. We hope that this research will inspire further studies and foster the development of practical applications across various related disciplines.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="16ea07d4eeb16e42cd765ae641bd5756" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240698,"asset_id":127518761,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240698/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518761"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518761"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518761; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="646910" id="papers"><div class="js-work-strip profile--work_container" data-work-id="127519330"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519330/Uncertain_Labeling_Graphs_and_Uncertain_Graph_Classes_with_Survey_for_Various_Uncertain_Sets_"><img alt="Research paper thumbnail of Uncertain Labeling Graphs and Uncertain Graph Classes (with Survey for Various Uncertain Sets)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519330/Uncertain_Labeling_Graphs_and_Uncertain_Graph_Classes_with_Survey_for_Various_Uncertain_Sets_">Uncertain Labeling Graphs and Uncertain Graph Classes (with Survey for Various Uncertain Sets)</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Graph theory, a branch of mathematics, studies the relationships between entities using vertices ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Graph theory, a branch of mathematics, studies the relationships between entities using vertices and edges. Uncertain Graph Theory has emerged within this field to model the uncertainties present in real-world networks. Graph labeling involves assigning labels, typically integers, to the vertices or edges of a graph according to specific rules or constraints. This paper introduces the concept of the Turiyam Neutrosophic Labeling Graph, which extends the traditional graph framework by incorporating four membership values—truth, indeterminacy, falsity, and a liberal state—at each vertex and edge. This approach enables a more nuanced representation of complex relationships. Additionally, we discuss the Single-Valued Pentapartitioned Neutrosophic Labeling Graph.The paper also examines the relationships between these novel graph concepts and other established types of graphs. In the Future Directions section, we propose several new classes of Uncertain Graphs and Labeling Graphs. And the appendix of this paper details the findings from an investigation into set concepts within Uncertain Theory. These set concepts have inspired numerous proposals and studies by various researchers, driven by their applications, mathematical properties, and research interests.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ff6a455ca8cbd806bf13631d7ec55895" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241201,"asset_id":127519330,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241201/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519330"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519330"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519330; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519321"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519321/Uncertain_Automata_and_Uncertain_Graph_Grammar"><img alt="Research paper thumbnail of Uncertain Automata and Uncertain Graph Grammar" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519321/Uncertain_Automata_and_Uncertain_Graph_Grammar">Uncertain Automata and Uncertain Graph Grammar</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Graph theory has been widely studied, resulting in numerous applications across various felds. Am...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Graph theory has been widely studied, resulting in numerous applications across various felds. Among its many topics, Automata and Graph Grammar have emerged as signifcant areas of research. This paper delves into these concepts, emphasizing their adaptation to uncertain frameworks like Fuzzy, Neutrosophic, Vague, Turiyam Neutrosophic, and Plithogenic systems. By integrating uncertainty into traditional graph theoretical models, the paper aims to address ongoing research challenges and expand the scope of these models.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="701d1811b09af01e4fe99ac13fff33de" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241190,"asset_id":127519321,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241190/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519321"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519321"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519321; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519309"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519309/Three_Novel_Approaches_to_Deep_Space_Interstellar_Travel_that_Transcend_the_Limitations_Imposed_by_the_Rocket_Equation"><img alt="Research paper thumbnail of Three Novel Approaches to Deep Space: Interstellar Travel that Transcend the Limitations Imposed by the Rocket Equation" class="work-thumbnail" src="https://attachments.academia-assets.com/121241179/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519309/Three_Novel_Approaches_to_Deep_Space_Interstellar_Travel_that_Transcend_the_Limitations_Imposed_by_the_Rocket_Equation">Three Novel Approaches to Deep Space: Interstellar Travel that Transcend the Limitations Imposed by the Rocket Equation</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In the past decades, there has been growing interest in novel approaches beyond existing technolo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In the past decades, there has been growing interest in novel approaches beyond existing technologies, especially to explore the Deep Space and beyond [1-3]. In this regard, the Tsiolkovsky rocket equation, a cornerstone of astronautics, provides a fundamental relationship between a spacecraft's initial mass, final mass, exhaust velocity, and the change in velocity it can achieve. While this equation has been instrumental in numerous space missions, it also presents inherent limitations that hinder our ability to explore the vast expanse of the universe [1]. One significant limitation of the Tsiolkovsky equation is the requirement for carrying propellant. The more propellant a spacecraft carries, the heavier it becomes, necessitating even more propellant to accelerate that increased mass. This creates a feedback loop that limits the maximum achievable velocity. As a result, long duration missions to distant destinations, such as Mars or beyond, become increasingly challenging and resource-intensive.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0e59448b7524ab2337ce47ad444e6e85" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241179,"asset_id":127519309,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241179/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519309"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519309"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519309; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519294"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519294/Symbolic_HyperPlithogenic_Set"><img alt="Research paper thumbnail of Symbolic HyperPlithogenic Set" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519294/Symbolic_HyperPlithogenic_Set">Symbolic HyperPlithogenic Set</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigate...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structured set defined by symbolic components 𝑃 𝑖 and coefficients 𝑎 𝑖 , enabling flexible algebraic operations under a specified prevalence order. In this paper, we examine concepts including the Symbolic HyperPlithogenic Set and the Symbolic 𝑛-SuperhyperPlithogenic Set.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="35129813d210e04261d65fd731c95a70" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241159,"asset_id":127519294,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241159/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519294"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519294"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519294; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519271"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519271/Survey_of_Planar_and_Outerplanar_Graphs_in_Fuzzy_and_Neutrosophic_Graphs"><img alt="Research paper thumbnail of Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519271/Survey_of_Planar_and_Outerplanar_Graphs_in_Fuzzy_and_Neutrosophic_Graphs">Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">As many readers may know, graph theory is a fundamental branch of mathematics that explores netwo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">As many readers may know, graph theory is a fundamental branch of mathematics that explores networks made up of nodes and edges, focusing on their paths, structures, and properties [196]. A planar graph is one that can be drawn on a plane without any edges intersecting, ensuring planarity. Outerplanar graphs, a subset of planar graphs, have all their vertices located on the boundary of the outer face in their planar embedding. In recent years, outerplanar graphs have been formally defined within the context of fuzzy graphs. To capture uncertain parameters and concepts, various graphs such as fuzzy, neutrosophic, Turiyam, and plithogenic graphs have been studied. In this paper, we investigate planar graphs, outerplanar graphs, apex graphs, and others within the frameworks of neutrosophic graphs, Turiyam Neutrosophic graphs, fuzzy graphs, and plithogenic graphs.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bcc700d388339bf94868255491be7d8b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241129,"asset_id":127519271,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241129/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519271"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519271"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519271; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519233"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519233/Superhypergraph_Neural_Networks_and_Plithogenic_Graph_Neural_Networks_Theoretical_Foundations"><img alt="Research paper thumbnail of Superhypergraph Neural Networks and Plithogenic Graph Neural Networks: Theoretical Foundations" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519233/Superhypergraph_Neural_Networks_and_Plithogenic_Graph_Neural_Networks_Theoretical_Foundations">Superhypergraph Neural Networks and Plithogenic Graph Neural Networks: Theoretical Foundations</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhyp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as Fuzzy Graphs and Neutrosophic Graphs have gained prominence. It is well established that Plithogenic Graphs serve as a generalization of both Fuzzy Graphs and Neutrosophic Graphs. Furthermore, the Fuzzy Graph Neural Network has been proposed and is an active area of research. This paper establishes the theoretical foundation for the development of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, expanding the applicability of neural networks to these advanced graph structures. While mathematical generalizations and proofs are presented, future computational experiments are anticipated.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="869d85180cf3f6077839dc1d698c1e47" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241116,"asset_id":127519233,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241116/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519233"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519233"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519233; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=127519233]").text(description); $(".js-view-count[data-work-id=127519233]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 127519233; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='127519233']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127519223"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127519223/Some_Types_of_HyperNeutrosophic_Set_7_Type_m_Nonstationary_Subset_valued_and_Complex_Refined"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127519223/Some_Types_of_HyperNeutrosophic_Set_7_Type_m_Nonstationary_Subset_valued_and_Complex_Refined">Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundational advancements introduced in [26,39-43]. The Neutrosophic S...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundational advancements introduced in [26,39-43]. The Neutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f070cdbdb10f40386464369eeb11258" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121241106,"asset_id":127519223,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121241106/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127519223"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127519223"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127519223; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518955"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518955/Some_Types_of_HyperNeutrosophic_Set_6_MultiNeutrosophic_Set_and_Refined_Neutrosophic_Set"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (6): MultiNeutrosophic Set and Refined Neutrosophic Set" class="work-thumbnail" src="https://attachments.academia-assets.com/121240865/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518955/Some_Types_of_HyperNeutrosophic_Set_6_MultiNeutrosophic_Set_and_Refined_Neutrosophic_Set">Some Types of HyperNeutrosophic Set (6): MultiNeutrosophic Set and Refined Neutrosophic Set</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds on the foundational advancements introduced in [22, 29-32]. The Neutrosophic Se...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds on the foundational advancements introduced in [22, 29-32]. The Neutrosophic Set provides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0fc5ab8ff17cb7a5d5088a6ff5453b6f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240865,"asset_id":127518955,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240865/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518955"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518955"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518955; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518945"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518945/Some_Types_of_HyperNeutrosophic_Set_5_Support_Paraconsistent_Faillibilist_and_Others"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others" class="work-thumbnail" src="https://attachments.academia-assets.com/121240854/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518945/Some_Types_of_HyperNeutrosophic_Set_5_Support_Paraconsistent_Faillibilist_and_Others">Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundational advancements introduced in [14, 25-27]. The Neutrosophic ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundational advancements introduced in [14, 25-27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20].</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="511a9198baad9c4ae38088e5255c97a8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240854,"asset_id":127518945,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240854/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518945"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518945"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518945; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518921"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518921/Some_Types_of_HyperNeutrosophic_Set_4_Cubic_Trapozoidal_q_Rung_Orthopair_Overset_Underset_and_Offset"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (4): Cubic, Trapozoidal, q-Rung Orthopair, Overset, Underset, and Offset" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518921/Some_Types_of_HyperNeutrosophic_Set_4_Cubic_Trapozoidal_q_Rung_Orthopair_Overset_Underset_and_Offset">Some Types of HyperNeutrosophic Set (4): Cubic, Trapozoidal, q-Rung Orthopair, Overset, Underset, and Offset</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundational work presented in [38-40]. The Neutrosophic Set provides ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundational work presented in [38-40]. The Neutrosophic Set provides a comprehensive mathematical framework for managing uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set, which are specifically designed to address increasingly complex and multidimensional problems. The formal definitions of these sets are available in [30]. In this paper, we extend the Neutrosophic Cubic Set, Trapezoidal Neutrosophic Set, q-Rung Orthopair Neutrosophic Set, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset using the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set. Furthermore, we briefly examine their properties and potential applications.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="18040d114c59f3b0f3d1c50666716b8e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240838,"asset_id":127518921,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240838/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518921"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518921"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518921; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518901"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518901/Some_Types_of_HyperNeutrosophic_Set_3_Dynamic_Quadripartitioned_Pentapartitioned_Heptapartitioned_m_polar"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, m-polar" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518901/Some_Types_of_HyperNeutrosophic_Set_3_Dynamic_Quadripartitioned_Pentapartitioned_Heptapartitioned_m_polar">Some Types of HyperNeutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, m-polar</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a ro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e522e63b5aa2201ea16d3753aee6e238" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240833,"asset_id":127518901,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240833/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518901"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518901"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518901; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518890"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518890/Some_Types_of_HyperNeutrosophic_Set_2_Complex_Single_Valued_Triangular_Fermatean_and_Linguistic_Sets"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, and Linguistic Sets" class="work-thumbnail" src="https://attachments.academia-assets.com/121240824/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518890/Some_Types_of_HyperNeutrosophic_Set_2_Complex_Single_Valued_Triangular_Fermatean_and_Linguistic_Sets">Some Types of HyperNeutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, and Linguistic Sets</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathe...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathematical framework for managing uncertainty, characterized by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to address more complex and multidimensional challenges. In this study, we extend the Complex Neutrosophic Set, Single-Valued Triangular Neutrosophic Set, Fermatean Neutrosophic Set, and Linguistic Neutrosophic Set within the frameworks of Hyperneutrosophic Sets and SuperHyperneutrosophic Sets. Furthermore, we investigate their mathematical structures and analyze their connections with other set-theoretic concepts.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="512e7aa440a8ce58e7708e435cf8c510" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240824,"asset_id":127518890,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240824/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518890"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518890"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518890; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518857"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518857/Some_Types_of_HyperNeutrosophic_Set_1_Bipolar_Pythagorean_Double_Valued_Interval_Valued_Set"><img alt="Research paper thumbnail of Some Types of HyperNeutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set" class="work-thumbnail" src="https://attachments.academia-assets.com/121240771/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518857/Some_Types_of_HyperNeutrosophic_Set_1_Bipolar_Pythagorean_Double_Valued_Interval_Valued_Set">Some Types of HyperNeutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by three membership functions: truth (T), indeterminacy (I), and falsity (F). In recent years, extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set have been introduced to address more complex scenarios. This paper proposes new concepts by extending Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets using the frameworks of Hyperneutrosophic and SuperHyperneutrosophic Sets. Additionally, a brief analysis of these extended concepts is presented.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45df8088343b9419a47c58571543e7b4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240771,"asset_id":127518857,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240771/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518857"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518857"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518857; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518840"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518840/Some_Graph_Parameters_for_Superhypertree_width_and_Neutrosophictree_width"><img alt="Research paper thumbnail of Some Graph Parameters for Superhypertree-width and Neutrosophictree-width" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518840/Some_Graph_Parameters_for_Superhypertree_width_and_Neutrosophictree_width">Some Graph Parameters for Superhypertree-width and Neutrosophictree-width</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Graph characteristics are often studied through various parameters, with ongoing research dedicat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Graph characteristics are often studied through various parameters, with ongoing research dedicated to exploring these aspects. Among these, graph width parameters-such as treewidthare particularly important due to their practical applications in algorithms and real-world problems. A hypergraph generalizes traditional graph theory by abstracting and extending its concepts [77]. More recently, the concept of a SuperHyperGraph has been introduced as a further generalization of the hypergraph. Neutrosophic logic [133], a mathematical framework, extends classical and fuzzy logic by allowing the simultaneous consideration of truth, indeterminacy, and falsity within an interval. In this paper, we explore Superhypertree-width, Neutrosophic treewidth, and t-Neutrosophic tree-width.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="170c36d829883e7ed1519f629afda0ad" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240758,"asset_id":127518840,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240758/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518840"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518840"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518840; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518821"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518821/Soft_Sets_Extensions_used_in_Bioinformatics"><img alt="Research paper thumbnail of Soft Sets Extensions used in Bioinformatics" class="work-thumbnail" src="https://attachments.academia-assets.com/121240744/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518821/Soft_Sets_Extensions_used_in_Bioinformatics">Soft Sets Extensions used in Bioinformatics</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This comprehensive review delves into the intricate realm of Soft Sets and their extensions, incl...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This comprehensive review delves into the intricate realm of Soft Sets and their extensions, including the HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, within the context of biomedical data analysis. Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518817"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518817/Significado_Neutros%C3%B3fico_Partes_comunes_de_cosas_poco_comunes_y_partes_poco_comunes_de_cosas_comunes"><img alt="Research paper thumbnail of Significado Neutrosófico: Partes comunes de cosas poco comunes y partes poco comunes de cosas comunes" class="work-thumbnail" src="https://attachments.academia-assets.com/121240735/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518817/Significado_Neutros%C3%B3fico_Partes_comunes_de_cosas_poco_comunes_y_partes_poco_comunes_de_cosas_comunes">Significado Neutrosófico: Partes comunes de cosas poco comunes y partes poco comunes de cosas comunes</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificaci...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificación de elementos comunes entre conceptos opuestos y en el análisis de las diferencias entre conceptos semejantes. En este contexto, se estudian las Partes Comunes a Cosas No Comunes, que se manifiestan cuando elementos como <A> y < antiA > comparten aspectos en su intersección, y las Partes No Comunes a Cosas Comunes, donde conceptos iguales como <A> y <B> difieren al exhibir elementos únicos. Este análisis permite comprender mejor la neutralidad e indeterminación representada por < neutA > y < neutB >, situados entre sus respectivos opuestos. La investigación abarca diversas áreas como la Dialéctica, el Yin Yang, y teorías sociales como el Capitalismo y el Socialismo, así como enfoques en Psicoanálisis y Psicología analítica, destacando la Intención paradójica en la comprensión de fenómenos y teorías, desde la Democracia hasta la Terapia cognitivo-conductual y la Terapia psicodinámica.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f8435eb72afc18a13fbed6bcb5e90200" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240735,"asset_id":127518817,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240735/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518817"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518817"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518817; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518796"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518796/Remark_on_Falaco_Soliton_as_a_Tunneling_Mechanism_in_a_Navier_Stokes_Universe"><img alt="Research paper thumbnail of Remark on Falaco Soliton as a Tunneling Mechanism in a Navier-Stokes Universe" class="work-thumbnail" src="https://attachments.academia-assets.com/121240719/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518796/Remark_on_Falaco_Soliton_as_a_Tunneling_Mechanism_in_a_Navier_Stokes_Universe">Remark on Falaco Soliton as a Tunneling Mechanism in a Navier-Stokes Universe</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is a follow up to our previous article [1] suggesting that it is possible to find tunn...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is a follow up to our previous article [1] suggesting that it is possible to find tunneling time solutions for Schrodinger equation considering quasicrystalline as interstellar matter, by virtue of quasicrystalline potential. The paper also discusses the mapping of these equations to Riccati equations, a class of nonlinear differential equations. This mapping can provide insights into the behavior of the Navier-Stokes equations and may lead to new methods for solving them. The Navier-Stokes equations, a set of nonlinear partial differential equations, are fundamental in fluid mechanics. They describe the motion of viscous fluids. In three dimensions, these equations are particularly complex and often leading to turbulence. The paper also discusses shortly on Falaco soliton as a tunneling mechanism in a Navier-Stokes Universe, which is quite able to fill the gap of realistic mechanism of quantum tunneling which is missing in standard Wave Mechanics. Further investigations are advised.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e842a232cdbe7195def29edc70ec4538" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240719,"asset_id":127518796,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240719/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518796"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518796"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518796; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127518761"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127518761/Reconsideration_of_Neutrosophic_Social_Science_and_Neutrosophic_Phenomenology_with_Non_classical_logic"><img alt="Research paper thumbnail of Reconsideration of Neutrosophic Social Science and Neutrosophic Phenomenology with Non-classical logic" class="work-thumbnail" src="https://attachments.academia-assets.com/121240698/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127518761/Reconsideration_of_Neutrosophic_Social_Science_and_Neutrosophic_Phenomenology_with_Non_classical_logic">Reconsideration of Neutrosophic Social Science and Neutrosophic Phenomenology with Non-classical logic</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering sign...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision-making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective p roblem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in fields such as social s ciences. By incorporating Neutrosophic Sets, we aim to improve their suitability for programming and mathematical analysis, providing advanced methods to tackle complex, multi-dimensional problems. We hope that this research will inspire further studies and foster the development of practical applications across various related disciplines.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="16ea07d4eeb16e42cd765ae641bd5756" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121240698,"asset_id":127518761,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121240698/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127518761"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127518761"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127518761; 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Are o redacție internațională și colaboratori din diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații. ***** Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ba732438733ec45dde74714df72f4fe2" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121122103,"asset_id":127383085,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121122103/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127383085"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127383085"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127383085; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127260645"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127260645/Superhypergraph_Neural_Networks_and_Plithogenic_Graph_Neural_Networks_Theoretical_Foundations"><img alt="Research paper thumbnail of Superhypergraph Neural Networks and Plithogenic Graph Neural Networks: Theoretical Foundations" class="work-thumbnail" src="https://attachments.academia-assets.com/121019598/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127260645/Superhypergraph_Neural_Networks_and_Plithogenic_Graph_Neural_Networks_Theoretical_Foundations">Superhypergraph Neural Networks and Plithogenic Graph Neural Networks: Theoretical Foundations</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span>Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond (Fifth Volume)</span><span>, 2025</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhyp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as Fuzzy Graphs and Neutrosophic Graphs have gained prominence. It is well established that Plithogenic Graphs serve as a generalization of both Fuzzy Graphs and Neutrosophic Graphs. Furthermore, the Fuzzy Graph Neural Network has been proposed and is an active area of research. This paper establishes the theoretical foundation for the development of SuperHyperGraph Neural Networks (SHGNNs) and Plithogenic Graph Neural Networks, expanding the applicability of neural networks to these advanced graph structures. While mathematical generalizations and proofs are presented, future computational experiments are anticipated.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0947c28f26cca4270ff4737cac5c7ee9" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":121019598,"asset_id":127260645,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/121019598/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127260645"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127260645"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127260645; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="127227674"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/127227674/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Sixth_volume_Various_New_Uncertain_Concepts_Collected_Papers_"><img alt="Research paper thumbnail of Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Sixth volume: Various New Uncertain Concepts (Collected Papers)." class="work-thumbnail" src="https://attachments.academia-assets.com/120992207/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127227674/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Sixth_volume_Various_New_Uncertain_Concepts_Collected_Papers_">Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Sixth volume: Various New Uncertain Concepts (Collected Papers).</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This book is the sixth volume in the series of Collected Papers on Advancing Uncertain Combinator...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This book is the sixth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Building upon the foundational contributions of previous volumes, this edition focuses on the exploration and development of Various New Uncertain Concepts, further enriching the study of uncertainty and complexity through innovative theoretical advancements and practical applications.<br />The volume is meticulously organized into 15 chapters, each presenting unique perspectives and contributions to the field. From theoretical explorations to real-world applications, these chapters provide a cohesive and comprehensive overview of the state of the art in uncertain combinatorics, emphasizing the versatility and power of the newly introduced concepts and methodologies. <br />The first chapter (SuperHypertree-depth – Structural Analysis in SuperHyperGraphs) explores the concept of SuperHypertree-depth, an extension of the classical graph parameter Tree-depth and its hypergraph counterpart Hypertree-depth. By introducing hierarchical nesting within SuperHyperGraphs, where both vertices and edges can represent recursive subsets, this study investigates the mathematical properties and structural implications of these extended parameters. The findings highlight the relationships between SuperHypertree-depth and its traditional graph-theoretic equivalents, providing a deeper understanding of their applicability to hierarchical and complex systems.<br />The second chapter (Obstructions for Hypertree-width and SuperHypertree-width) examines the role of ultrafilters as obstructions in determining Hypertree-width and extends the concept to SuperHypertree-width. Building on hypergraph theory, which abstracts traditional graph frameworks into more complex domains, the study investigates how recursive structures within SuperHyperGraphs redefine the computational and structural properties of these parameters. Ultrafilters, with their broad mathematical significance, serve as critical tools for understanding the limitations and potentials of these advanced graph metrics.<br />The third chapter (SuperHypertree-Length and SuperHypertree-Breadth in SuperHyperGraphs) investigates the extension of the graph-theoretic parameters Tree-length and Tree-breadth to the realms of hypergraphs and SuperHyperGraphs. By leveraging the hierarchical nesting of SuperHyperGraphs, the study explores how these parameters adapt to increasingly complex and multi-level structures. Comparative analyses between these extended parameters and their classical counterparts reveal new insights into their relevance and utility in advanced graph and hypergraph theory.<br />Plithogenic Sets, which generalize Fuzzy and Neutrosophic Sets, are extended in the fourth chapter (Extended HyperPlithogenic Sets and Generalized Plithogenic Graphs) to Extended Plithogenic Sets, HyperPlithogenic Sets, and SuperHyperPlithogenic Sets. This study further investigates their application to graph theory through the concepts of Extended Plithogenic Graphs and Generalized Extended Plithogenic Graphs. The chapter provides a concise exploration of these frameworks, offering insights into their potential for addressing uncertainty and complexity in graph structures.  <br />Soft Sets provide an effective framework for decision-making by mapping parameters to subsets of a universal set, addressing uncertainty and vagueness. The fifth chapter (Double-Framed Superhypersoft Set and Double-Framed Treesoft Set) introduces the Double-Framed SuperHypersoft Set and the Double-Framed Treesoft Set as extensions of traditional and advanced soft set frameworks, such as Hypersoft and SuperHypersoft Sets. The chapter explores their relationships with existing concepts, offering new tools to handle complex decision-making scenarios with enhanced structural flexibility.<br />The sixth paper (HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set) introduces the concepts of the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set, which extend the Plithogenic Cubic Set by integrating both interval-valued and single-valued fuzzy memberships. These sets leverage multi-attribute aggregation techniques inherent to plithogenic structures, allowing for nuanced representations of uncertainty. Additionally, related constructs such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set are explored, further enriching the theoretical and practical applications of this framework.<br />The seventh chapter (L-Neutrosophic Sets and Nonstationary Neutrosophic Sets) extends the foundational concepts of fuzzy sets by integrating Neutrosophic and Plithogenic frameworks. By introducing L-Neutrosophic Sets and Nonstationary Neutrosophic Sets, the study enhances the representation of uncertainty through independent membership components: truth, indeterminacy, and falsity. These advanced constructs also incorporate multi-dimensional and contradictory attributes, providing a robust means of modeling complex decision-making and uncertain data.<br />Plithogenic and Rough Sets, known for generalizing uncertainty modeling and classification, are extended in the eight chapter (Forest HyperPlithogenic and Forest HyperRough Sets) to Forest HyperPlithogenic Sets, Forest SuperHyperPlithogenic Sets, Forest HyperRough Sets, and Forest SuperHyperRough Sets. These frameworks incorporate hierarchical and recursive structures to advance existing set-theoretic paradigms. The chapter explores their applications in multi-level data analysis and uncertainty classification, demonstrating their adaptability to complex systems.<br />Building on Fuzzy, Neutrosophic, and Plithogenic Sets, the tenth chapter (Symbolic HyperPlithogenic Sets) introduces Symbolic HyperPlithogenic Sets and Symbolic n-SuperHyperPlithogenic Sets. These sets incorporate symbolic components and algebraic coefficients, enabling flexible operations within a defined prevalence order. By extending symbolic representation into hyperplithogenic and superhyperplithogenic domains, the chapter opens new pathways for addressing uncertainty and hierarchical complexity in mathematical modeling.  <br />Soft Sets, designed to manage uncertainty and imprecision, have evolved through various extensions like Hypersoft Sets and SuperHypersoft Sets. The eleventh chapter (N-SuperHypersoft and Bijective SuperHypersoft Sets) introduces N-SuperHypersoft Sets, N-Treesoft Sets, Bijective SuperHypersoft Sets, and Bijective Treesoft Sets. These new constructs enhance decision-making frameworks by incorporating advanced hierarchical and bijective relationships, building on existing theories and expanding their applications.<br />Plithogenic Sets, known for integrating multi-valued attributes and contradictions, and Rough Sets, which partition data into definable approximations, are combined in the twelfth chapter (Plithogenic Rough Sets) to form Plithogenic Rough Sets. This fusion provides a powerful framework for addressing uncertainty in dynamic and complex decision-making scenarios, offering a novel approach to uncertainty modeling.<br />Expanding on Neutrosophic Sets, which represent truth, indeterminacy, and falsehood, this chapter introduces Plithogenic Duplets and Plithogenic Triplets. These constructs leverage the Plithogenic framework to incorporate attributes, values, and contradiction measures. The thirteenth chapter (Plithogenic Duplets and Triplets) examines their relationships with Neutrosophic Duplets and Triplets, offering new tools for multi-dimensional data representation and decision-making.<br />Building on foundational concepts like Rough Sets and Vague Sets, the fourteenth chapter (SuperRough and SuperVague Sets) introduces SuperRough Sets and SuperVague Sets. These generalized frameworks extend uncertainty modeling by incorporating hierarchical structures. The study also demonstrates that SuperRough Sets can evolve into SuperHyperRough Sets, providing further generalizations for advanced data classification and analysis.<br />The fifteenth chapter (Neutrosophic TreeSoft Expert and ForestSoft Sets) revisits the Neutrosophic TreeSoft Set, which combines the hierarchical structure of TreeSoft Sets with the Neutrosophic framework for uncertainty representation. Additionally, it introduces the Neutrosophic TreeSoft Expert Set, incorporating expert knowledge into the model. The chapter also explores the ForestSoft Set and its extension, the Neutrosophic ForestSoft Set, to provide multi-level, tree-structured approaches for complex data representation and analysis.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ace1307ff5a0d4ef7c75014d22e56cb0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120992207,"asset_id":127227674,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120992207/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127227674"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127227674"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127227674; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=127227674]").text(description); $(".js-view-count[data-work-id=127227674]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 127227674; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='127227674']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ace1307ff5a0d4ef7c75014d22e56cb0" } } $('.js-work-strip[data-work-id=127227674]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":127227674,"title":"Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. 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Fifth volume: Various SuperHyperConcepts (Collected Papers)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127227638/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Fifth_volume_Various_SuperHyperConcepts_Collected_Papers_">Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Fifth volume: Various SuperHyperConcepts (Collected Papers)</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This book is the fifth volume in the series of Collected Papers on Advancing Uncertain Combinator...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This book is the fifth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of Various SuperHyperConcepts, building on the foundational advancements introduced in previous volumes.<br />The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough set theories, providing robust frameworks to model and analyze the inherent complexity of real-world uncertainties.<br />At the heart of this series lies combinatorics and set theory—cornerstones of mathematics that address the study of counting, arrangements, and the relationships between collections under defined rules. Traditionally, combinatorics has excelled in solving problems involving uncertainty, while advancements in set theory have expanded its scope to include powerful constructs like fuzzy and neutrosophic sets. These advanced sets bring new dimensions to uncertainty modeling by capturing not just binary truth but also indeterminacy and falsity.<br />In this fifth volume, the exploration of Various SuperHyperConcepts provides an innovative lens to address uncertainty, complexity, and hierarchical relationships. It synthesizes key methodologies introduced in earlier volumes, such as hyperization and neutrosophic extensions, while advancing new theories and applications. From pioneering hyperstructures to applications in advanced decision-making, language modeling, and neural networks, this book represents a significant leap forward in uncertain combinatorics and its practical implications across disciplines.<br /><br />The book is structured into 17 chapters, each contributing unique perspectives and advancements in the realm of Various SuperHyperConcepts and their related frameworks:<br />Chapter 1 introduces the concept of Body-Mind-Soul-Spirit Fluidity within psychology and phenomenology, while examining established social science frameworks like PDCA and DMAIC. It extends these frameworks using Neutrosophic Sets, a flexible extension of Fuzzy Sets, to improve their adaptability for mathematical and programming applications. The chapter emphasizes the potential of Neutrosophic theory to address multi-dimensional challenges in social sciences.<br />Chapter 2 delves into the theoretical foundation of Hyperfunctions and their generalizations, such as Hyperrandomness and Hyperdecision-Making. It explores higher-order frameworks like Weak Hyperstructures, Hypergraphs, and Cognitive Hypermaps, aiming to establish their versatility in addressing multi-layered problems and setting a foundation for further studies.<br />Chapter 3 extends traditional decision-making methodologies into HyperDecision-Making and n-SuperHyperDecision-Making. By building on approaches like MCDM and TOPSIS, this chapter develops frameworks capable of addressing complex decision-making scenarios, emphasizing their applicability in dynamic, multi-objective contexts.<br />Chapter 4 explores integrating uncertainty frameworks, including Fuzzy, Neutrosophic, and Plithogenic Sets, into Large Language Models (LLMs). It proposes innovative models like Large Uncertain Language Models and Natural Uncertain Language Processing, integrating hierarchical and generalized structures to advance the handling of uncertainty in linguistic representation and processing.<br />Chapter 5 introduces the Natural n-Superhyper Plithogenic Language by synthesizing natural language, plithogenic frameworks, and superhyperstructures. This innovative construct seeks to address challenges in advanced linguistic and structural modeling, blending attributes of uncertainty, complexity, and hierarchical abstraction.<br />Chapter 6 defines mathematical extensions such as NeutroHyperstructures and AntiHyperstructures using the Neutrosophic Triplet framework. It formalizes structures like neutro-superhyperstructures, advancing classical frameworks into higher-dimensional realms.<br />Chapter 7 explores the extension of Binary Code, Gray Code, and Floorplans through hyperstructures and superhyperstructures. It highlights their iterative and hierarchical applications, demonstrating their adaptability for complex data encoding and geometric arrangement challenges.<br />Chapter 8 investigates the Neutrosophic TwoFold SuperhyperAlgebra, combining classical algebraic operations with neutrosophic components. This chapter expands upon existing algebraic structures like Hyperalgebra and AntiAlgebra, exploring hybrid frameworks for advanced mathematical modeling.<br />Chapter 9 introduces Hyper Z-Numbers and SuperHyper Z-Numbers by extending the traditional Z-Number framework with hyperstructures. These extensions aim to represent uncertain information in more complex and multidimensional contexts.<br />Chapter 10 revisits category theory through the lens of hypercategories and superhypercategories. By incorporating hierarchical and iterative abstractions, this chapter extends the foundational principles of category theory to more complex and layered structures.<br />Chapter 11 formalizes the concept of n-SuperHyperBranch-width and its theoretical properties. By extending hypergraphs into superhypergraphs, the chapter explores recursive structures and their potential for representing intricate hierarchical relationships.<br />Chapter 12 examines superhyperstructures of partitions, integrals, and spaces, proposing a framework for advancing mathematical abstraction. It highlights the potential applications of these generalizations in addressing hierarchical and multi-layered problems.<br />Chapter 13 revisits Rough, HyperRough, and SuperHyperRough Sets, introducing new concepts like Tree-HyperRough Sets. The chapter connects these frameworks to advanced approaches for modeling uncertainty and complex relationships.<br />Chapter 14 explores Plithogenic SuperHyperStructures and their applications in decision-making, control, and neuro systems. By integrating these advanced frameworks, the chapter proposes innovative directions for extending existing systems to handle multi-attribute and contradictory properties.<br />Chapter 15 focuses on superhypergraphs, expanding hypergraph concepts to model complex structural types like arboreal and molecular superhypergraphs. It introduces Generalized n-th Powersets as a unifying framework for broader mathematical applications, while also touching on hyperlanguage processing.<br />Chapter 16 defines NeutroHypergeometry and AntiHypergeometry as extensions of classical geometric structures. Using the Geometric Neutrosophic Triplet, the chapter demonstrates the flexibility of these frameworks in representing multi-dimensional and uncertain relationships.<br />Chapter 17 establishes the theoretical groundwork for SuperHyperGraph Neural Networks and Plithogenic Graph Neural Networks. By integrating advanced graph structures, this chapter opens pathways for applying neural networks to more intricate and uncertain data representations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="962d67b10e296edfc51126c3e844fd94" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120992151,"asset_id":127227638,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120992151/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127227638"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127227638"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127227638; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=127227638]").text(description); $(".js-view-count[data-work-id=127227638]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 127227638; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='127227638']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "962d67b10e296edfc51126c3e844fd94" } } $('.js-work-strip[data-work-id=127227638]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":127227638,"title":"Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. 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Fourth volume: HyperUncertain Set (Collected Papers)" class="work-thumbnail" src="https://attachments.academia-assets.com/120991889/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/127227296/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Fourth_volume_HyperUncertain_Set_Collected_Papers_">Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Fourth volume: HyperUncertain Set (Collected Papers)</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This book represents the fourth volume in the series Collected Papers on Advancing Uncertain Comb...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This book represents the fourth volume in the series Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of the HyperUncertain Set, building on the foundational advancements introduced in previous volumes.<br />The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough set theories, providing robust frameworks to model and analyze the inherent complexity of real-world uncertainties.<br />At the heart of this series lies combinatorics and set theory—cornerstones of mathematics that address the study of counting, arrangements, and the relationships between collections under defined rules. Traditionally, combinatorics has excelled in solving problems involving uncertainty, while advancements in set theory have expanded its scope to include powerful constructs like fuzzy and neutrosophic sets. These advanced sets bring new dimensions to uncertainty modeling by capturing not just binary truth but also indeterminacy and falsity.<br />In this fourth volume, the integration of set theory with graph theory takes center stage, culminating in "graphized" structures such as hypergraphs and superhypergraphs. These structures, paired with innovations like Neutrosophic Oversets, Undersets, Offsets, and the Nonstandard Real Set, extend the boundaries of mathematical abstraction. This fusion of combinatorics, graph theory, and uncertain set theory creates a rich foundation for addressing the multidimensional and hierarchical uncertainties prevalent in both theoretical and applied domains.<br />The book is structured into thirteen chapters, each contributing unique perspectives and advancements in the realm of HyperUncertain Sets and their related frameworks.<br /><br />The first chapter (Advancing Traditional Set Theory with Hyperfuzzy, Hyperneutrosophic, and Hyperplithogenic Sets) explores the evolution of classical set theory to better address the complexity and ambiguity of real-world phenomena. By introducing hierarchical structures like hyperstructures and superhyperstructures—created through iterative applications of power sets—it lays the groundwork for more abstract and adaptable mathematical tools. The focus is on extending three foundational frameworks: Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets into their hyperforms: Hyperfuzzy Sets, Hyperneutrosophic Sets, and Hyperplithogenic Sets. These advanced concepts are applied across diverse fields such as statistics, clustering, evolutionary theory, topology, decision-making, probability, and language theory. The goal is to provide a robust platform for future research in this expanding area of study.<br />The second chapter (Applications and Mathematical Properties of Hyperneutrosophic and SuperHyperneutrosophic Sets) extends the work on Hyperfuzzy, Hyperneutrosophic, and Hyperplithogenic Sets by delving into their advanced applications and mathematical foundations. Building on prior research, it specifically examines Hyperneutrosophic and SuperHyperneutrosophic Sets, exploring their integration into: Neutrosophic Logic, Cognitive Maps,Graph Neural Networks, Classifiers, and Triplet Groups. The chapter also investigates their mathematical properties and applicability in addressing uncertainties and complexities inherent in various domains. These insights aim to inspire innovative uses of hypergeneralized sets in modern theoretical and applied research.<br />The third chapter (New Extensions of Hyperneutrosophic Sets – Bipolar, Pythagorean, Double-Valued, and Interval-Valued Sets) studies advanced variations of Neutrosophic Sets, a mathematical framework defined by three membership functions: truth (T), indeterminacy (I), and falsity (F). By leveraging the concepts of Hyperneutrosophic and SuperHyperneutrosophic Sets, the study extends: Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets. These extensions address increasingly complex scenarios, and a brief analysis is provided to explore their potential applications and mathematical underpinnings.<br />Building on prior research, the fourth chapter (Hyperneutrosophic Extensions of Complex, Single-Valued Triangular, Fermatean, and Linguistic Sets) expands on Neutrosophic Set theory by incorporating recent advancements in Hyperneutrosophic and SuperHyperneutrosophic Sets. The study focuses on extending: Complex Neutrosophic Sets, Single-Valued Triangular Neutrosophic Sets, Fermatean Neutrosophic Sets, and Linguistic Neutrosophic Sets. The analysis highlights the mathematical structures of these hyperextensions and explores their connections with existing set-theoretic concepts, offering new insights into managing uncertainty in multidimensional challenges.<br />The fifth chapter (Advanced Extensions of Hyperneutrosophic Sets – Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, and m-Polar) delves deeper into the evolution of Neutrosophic Sets by exploring advanced frameworks designed for even more intricate applications. New extensions include: Dynamic Neutrosophic Sets, Quadripartitioned Neutrosophic Sets, Pentapartitioned Neutrosophic Sets, Heptapartitioned Neutrosophic Sets, and m-Polar Neutrosophic Sets. These developments build upon foundational research and aim to provide robust tools for addressing multidimensional and highly nuanced problems.<br />The sixth chapter (Advanced Extensions of Hyperneutrosophic Sets – Cubic, Trapezoidal, q-Rung Orthopair, Overset, Underset, and Offset) builds upon the Neutrosophic framework, which employs truth (T), indeterminacy (I), and falsity (F) to address uncertainty. Leveraging advancements in Hyperneutrosophic and SuperHyperneutrosophic Sets, the study extends: Cubic Neutrosophic Sets, Trapezoidal Neutrosophic Sets, q-Rung Orthopair Neutrosophic Sets, Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets. The chapter provides a brief analysis of these new set types, exploring their properties and potential applications in solving multidimensional problems.<br />The seventh chapter (Specialized Classes of Hyperneutrosophic Sets – Support, Paraconsistent, and Faillibilist Sets) delves into unique classes of Neutrosophic Sets extended through Hyperneutrosophic and SuperHyperneutrosophic frameworks to tackle advanced theoretical challenges. The study introduces and extends: Support Neutrosophic Sets, Neutrosophic Intuitionistic Sets, Neutrosophic Paraconsistent Sets, Neutrosophic Faillibilist Sets, Neutrosophic Paradoxist and Pseudo-Paradoxist Sets, Neutrosophic Tautological and Nihilist Sets, Neutrosophic Dialetheist Sets, and Neutrosophic Trivialist Sets. These extensions address highly nuanced aspects of uncertainty, further advancing the theoretical foundation of Neutrosophic mathematics.<br />The eight chapter (MultiNeutrosophic Sets and Refined Neutrosophic Sets) focuses on two advanced Neutrosophic frameworks: MultiNeutrosophic Sets, and Refined Neutrosophic Sets. Using Hyperneutrosophic and nn-SuperHyperneutrosophic Sets, these extensions are analyzed in detail, highlighting their adaptability to multidimensional and complex scenarios. Examples and mathematical properties are provided to showcase their practical relevance and theoretical depth.<br />The ninth chapter (Advanced Hyperneutrosophic Set Types – Type-m, Nonstationary, Subset-Valued, and Complex Refined) explores extensions of the Neutrosophic framework, focusing on: Type-m Neutrosophic Sets, Nonstationary Neutrosophic Sets, Subset-Valued Neutrosophic Sets, and Complex Refined Neutrosophic Sets. These extensions utilize the Hyperneutrosophic and SuperHyperneutrosophic frameworks to address advanced challenges in uncertainty management, expanding their mathematical scope and practical applications.<br />The tenth chapter (Hyperfuzzy Hypersoft Sets and Hyperneutrosophic Hypersoft Sets) integrates the principles of Fuzzy, Neutrosophic, and Soft Sets with hyperstructures to introduce: Hyperfuzzy Hypersoft Sets, and Hyperneutrosophic Hypersoft Sets. These frameworks are designed to manage complex uncertainty through hierarchical structures based on power sets, with detailed analysis of their properties and theoretical potential.<br />The eleventh chapter (A Review of SuperFuzzy, SuperNeutrosophic, and SuperPlithogenic Sets) revisits and extends the study of advanced set concepts such as: SuperFuzzy Sets, Super-Intuitionistic Fuzzy Sets,Super-Neutrosophic Sets, and SuperPlithogenic Sets,<br />including their specialized variants like quadripartitioned, pentapartitioned, and heptapartitioned forms. The work serves as a consolidation of existing studies while highlighting potential directions for future research in hierarchical uncertainty modeling.<br />Focusing on decision-making under uncertainty, the tweve chapter (Advanced SuperHypersoft and TreeSoft Sets) introduces six novel concepts: SuperHypersoft Rough Sets,SuperHypersoft Expert Sets, Bipolar SuperHypersoft Sets, TreeSoft Rough Sets, TreeSoft Expert Sets, and Bipolar TreeSoft Sets. Definitions, properties, and potential applications of these frameworks are explored to enhance the flexibility of soft set-based models.<br />The final chapter (Hierarchical Uncertainty in Fuzzy, Neutrosophic, and Plithogenic Sets) provides a comprehensive survey of hierarchical uncertainty frameworks, with a focus on Plithogenic Sets and their advanced extensions: Hyperplithogenic Sets, SuperHyperplithogenic Sets. It examines relationships with other major concepts such as Intuitionistic Fuzzy Sets, Vague Sets, Picture Fuzzy Sets, Hesitant Fuzzy Sets, and multi-partitioned Neutrosophic Sets, consolidating their theoretical interconnections for modeling complex systems.<br />This volume not only reflects the dynamic...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="52131c86b0c19866924709f7fca739f8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120991889,"asset_id":127227296,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120991889/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="127227296"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="127227296"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 127227296; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=127227296]").text(description); $(".js-view-count[data-work-id=127227296]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 127227296; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='127227296']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "52131c86b0c19866924709f7fca739f8" } } $('.js-work-strip[data-work-id=127227296]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":127227296,"title":"Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. 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Are o redacție internațională și colaboratori din diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații. ***** Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="693c87ba2cc5b546940d685f08b82666" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120502234,"asset_id":126657554,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120502234/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="126657554"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="126657554"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126657554; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126657554]").text(description); $(".js-view-count[data-work-id=126657554]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126657554; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126657554']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "693c87ba2cc5b546940d685f08b82666" } } $('.js-work-strip[data-work-id=126657554]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126657554,"title":"Constelatii Diamantine, Nr. 173, 2025","internal_url":"https://www.academia.edu/126657554/Constelatii_Diamantine_Nr_173_2025","owner_id":4976797,"coauthors_can_edit":true,"owner":{"id":4976797,"first_name":"Florentin","middle_initials":null,"last_name":"Smarandache","page_name":"FlorentinSmarandache","domain_name":"unm","created_at":"2013-07-28T11:35:34.896-07:00","display_name":"Florentin Smarandache","url":"https://unm.academia.edu/FlorentinSmarandache"},"attachments":[{"id":120502234,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/120502234/thumbnails/1.jpg","file_name":"Constelatii_diamantine_nr_173_2025.pdf","download_url":"https://www.academia.edu/attachments/120502234/download_file","bulk_download_file_name":"Constelatii_Diamantine_Nr_173_2025.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/120502234/Constelatii_diamantine_nr_173_2025-libre.pdf?1735492957=\u0026response-content-disposition=attachment%3B+filename%3DConstelatii_Diamantine_Nr_173_2025.pdf\u0026Expires=1739480826\u0026Signature=FdrA0UMbv7ls8HvVzfkljhXc2MgAhDkznWYaew8fvCUrawbJjTqGMHHhcWU7xW1uCKo9WJ~UaCQ42D0p7CxefcvhiehpSQgl26EYkgATSfTiZFKBMlvWLhoFCR3UfksJdRs4jRWZAE2Y7RtcvCjlt1kyYPFOR~TVzu3nziVVvaERc9SB6LpvPTLq0GASyfcC5mpiKJ3jQV6VxdVHGIfhRhQl~rdvI5GiAzS7E87XtCjLFy5YZ8aDZKdXBvWneTf6880qtcg7v3hPaanvdSIlquXRu6GWPzTJfD3RptjfWX6kSyI3isWZSPnnsb9vAHK~kFCnZXubiK4rNlZnyNReSA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="126136096"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/126136096/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Second_volume"><img alt="Research paper thumbnail of Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Second volume" class="work-thumbnail" src="https://attachments.academia-assets.com/120060162/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/126136096/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Second_volume">Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Second volume</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and U...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels in handling uncertainty, while set theory has evolved with concepts such as fuzzy and neutrosophic sets, which enable the modeling of complex real-world uncertainties by addressing truth, indeterminacy, and falsehood. These advancements, when combined with graph theory, give rise to novel forms of uncertain sets in "graphized" structures, including hypergraphs and superhypergraphs. Innovations such as Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing both theoretical and practical boundaries. The synthesis of combinatorics, set theory, and graph theory in this volume provides a robust framework for addressing the complexities and uncertainties inherent in both mathematical and real-world systems, paving the way for future research and application.<br />In the first chapter, “A Review of the Hierarchy of Plithogenic, Neutrosophic, and Fuzzy Graphs: Survey and Applications”, the authors investigate the interrelationships among various graph classes, including Plithogenic graphs, and explore other related structures. Graph theory, a fundamental branch of mathematics, focuses on networks of nodes and edges, studying their paths, structures, and properties. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, representing the level of uncertainty. The Turiyam Neutrosophic Graph is introduced as an extension of both Neutrosophic and Fuzzy Graphs, while Plithogenic graphs offer a potent method for managing uncertainty.<br />The second chapter, “Review of Some Superhypergraph Classes: Directed, Bidirected, Soft, and Rough”, examines advanced graph structures such as directed superhypergraphs, bidirected hypergraphs, soft superhypergraphs, and rough superhypergraphs. Classical graph classes include undirected graphs, where edges lack orientation, and directed graphs, where edges have specific directions. Recent innovations, including bidirected graphs, have sparked ongoing research and significant advancements in the field. Soft Sets and their extension to Soft Graphs provide a flexible framework for managing uncertainty, while Rough Sets and Rough Graphs address uncertainty by using lower and upper approximations to handle imprecise data. Hypergraphs generalize traditional graphs by allowing edges, or hyperedges, to connect more than two vertices. Superhypergraphs further extend this by allowing both vertices and edges to represent subsets, facilitating the modeling of hierarchical and group-based relationships.<br />The third chapter, “Survey of Intersection Graphs, Fuzzy Graphs, and Neutrosophic Graphs”, explores the intersection graph models within the realms of Fuzzy Graphs, Intuitionistic Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. The chapter highlights their mathematical properties and interrelationships, reflecting the growing number of graph classes being developed in these areas. Intersection graphs, such as Unit Square Graphs, Circle Graphs, and Ray Intersection Graphs, are crucial for understanding complex graph structures in uncertain environments.<br />The fourth chapter, “Fundamental Computational Problems and Algorithms for SuperHyperGraphs”, addresses optimization problems within the SuperHypergraph framework, such as the SuperHypergraph Partition Problem, Reachability, and Minimum Spanning SuperHypertree. The chapter also adapts classical problems like the Traveling Salesman Problem and the Chinese Postman Problem to the SuperHypergraph context, exploring how hypergraphs, which allow hyperedges to connect more than two vertices, can be used to solve complex hierarchical and relational problems.<br />The fifth chapter, “A Short Note on the Basic Graph Construction Algorithm for Plithogenic Graphs”, delves into algorithms designed for Plithogenic Graphs and Intuitionistic Plithogenic Graphs, analyzing their complexity and validity. Plithogenic Graphs model multi-valued attributes by incorporating membership and contradiction functions, offering a nuanced representation of complex relationships.<br />The sixth chapter, “Short Note of Bunch Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs”, generalizes traditional graph theory by representing nodes as groups (bunches) rather than individual entities. This approach enables the modeling of both competition and collaboration within a network. The chapter explores various uncertain models of bunch graphs, including Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs.<br />In the seventh chapter, “A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs”, the authors extend several fuzzy graph classes to Neutrosophic graphs and analyze their properties. Neutrosophic Graphs, a generalization of fuzzy graphs, incorporate degrees of truth, indeterminacy, and falsity to model uncertainty more effectively.<br />The eighth chapter, “Short Note of Even-Hole-Graph for Uncertain Graph”, focuses on Even-Hole-Free and Meyniel Graphs analyzed within the frameworks of Fuzzy, Neutrosophic, Turiyam Neutrosophic, and Plithogenic Graphs. The study investigates the structure of these graphs, with an emphasis on their implications for uncertainty modeling.<br />The ninth chapter, “Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs”, explores planar and outerplanar graphs, as well as apex graphs, within the contexts of fuzzy, neutrosophic, Turiyam Neutrosophic, and plithogenic graphs. The chapter examines how these types of graphs are used to model uncertain parameters and relationships in mathematical and real-world systems.<br />The tenth chapter, “General Plithogenic Soft Rough Graphs and Some Related Graph Classes”, introduces and explores new concepts such as Turiyam Neutrosophic Soft Graphs and General Plithogenic Soft Graphs. The chapter also examines models of uncertain graphs, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, all designed to handle uncertainty in diverse contexts.<br />The eleventh chapter, “Survey of Trees, Forests, and Paths in Fuzzy and Neutrosophic Graphs”, provides a comprehensive study of Trees, Forests, and Paths within the framework of Fuzzy and Neutrosophic Graphs. This chapter focuses on classifying and analyzing graph structures like trees and paths in uncertain environments, contributing to the ongoing development of graph theory in the context of uncertainty.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="290b3488dea6257a1087368b3f350cff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120060162,"asset_id":126136096,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120060162/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="126136096"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="126136096"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126136096; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126136096]").text(description); $(".js-view-count[data-work-id=126136096]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126136096; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126136096']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "290b3488dea6257a1087368b3f350cff" } } $('.js-work-strip[data-work-id=126136096]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126136096,"title":"Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. 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Third volume" class="work-thumbnail" src="https://attachments.academia-assets.com/120060029/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/126136003/Advancing_Uncertain_Combinatorics_through_Graphization_Hyperization_and_Uncertainization_Fuzzy_Neutrosophic_Soft_Rough_and_Beyond_Third_volume">Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. Third volume</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://gunma-u.academia.edu/TakaakiFujita">Takaaki Fujita</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The third volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Un...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The third volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents an in-depth exploration of the cutting-edge developments in uncertain combinatorics and set theory. This comprehensive collection highlights innovative methodologies such as graphization, hyperization, and uncertainization, which enhance combinatorics by incorporating foundational concepts from fuzzy, neutrosophic, soft, and rough set theories. These advancements open new mathematical horizons, offering novel approaches to managing uncertainty within complex systems.<br />Combinatorics, a discipline focused on counting, arrangement, and structure, often faces challenges when uncertainty is present. Set theory, which underpins combinatorial problems, has evolved to tackle these challenges. The introduction of fuzzy and neutrosophic sets has expanded the toolkit for modeling uncertainty by incorporating elements of truth, indeterminacy, and falsehood into decision-making processes. These innovations seamlessly intersect with graph theory, providing new ways to represent uncertain structures through "graphized" forms such as hypergraphs and superhypergraphs.<br />This volume also introduces advanced concepts like Neutrosophic Oversets, Undersets, and Offsets, which push the boundaries of classical graph theory and offer deeper insights into the mathematical and practical challenges posed by real-world systems. By blending combinatorics, set theory, and graph theory, the authors have created a robust framework for addressing uncertainty in both mathematical systems and their real-world applications. This foundation sets the stage for future breakthroughs in combinatorics, set theory, and related fields.<br />Each chapter in this volume contributes both theoretical foundations and practical applications, demonstrating the power of integrating graph theory, set theory, and uncertainty models. The new ideas, algorithms, and mathematical tools presented here will drive the future of combinatorial research and its applications in uncertain environments.<br />In the first chapter, “Introduction to Upside-Down Logic: Its Deep Relation to Neutrosophic Logic and Applications”, the authors present Upside-Down Logic, a novel logical framework that systematically transforms truths into falsehoods and vice versa, based on contextual shifts. Introduced by F. Smarandache, this paper provides a mathematical definition of Upside-Down Logic, including applications related to the Japanese language. The chapter also introduces Contextual Upside-Down Logic, an extension that adjusts logical connectives alongside flipped truth values, as well as Indeterm-Upside-Down Logic and Certain Upside-Down Logic to address indeterminacy. A simple algorithm is also proposed to demonstrate the computational aspects of this logic.<br />In the second chapter, “Local-Neutrosophic Logic and Local-Neutrosophic Sets: Incorporating Locality with Applications”, the authors introduce Local-Neutrosophic Logic and Local-Neutrosophic Sets, which integrate the concept of locality into Neutrosophic Logic. By defining locality as the influence of immediate surroundings on an object or system, this chapter explores how it affects indeterminacy in real-world problems. The paper also examines potential applications and provides mathematical definitions for these new concepts.<br />The third chapter, “A Review of Fuzzy and Neutrosophic Offsets: Connections to Some Set Concepts and Normalization Function”, extends the concept of offsets in uncertain set-theoretic frameworks, such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets. This chapter introduces several advanced types of offsets, including Nonstationary Fuzzy Offset, Multi-valued Plithogenic Offset, and Subset-valued Neutrosophic Offset, offering deeper insights into handling uncertainty in mathematical models.<br />In the fourth chapter, “Review of Plithogenic Directed, Mixed, Bidirected, and Pangene OffGraph”, the authors build upon Plithogenic Graphs to propose extensions such as Plithogenic Directed OffGraph, Plithogenic BiDirected OffGraph, and Plithogenic Mixed OffGraph. These new concepts, including the Plithogenic Pangene OffGraph, are explored in detail, with a focus on their mathematical properties and potential applications in uncertain graph theory.<br />The fifth chapter, “Short Note on Neutrosophic Closure Matroids”, explores the extension of matroid concepts into Neutrosophic and Turiyam Neutrosophic set theories, introducing Neutrosophic closure matroids. This concept integrates uncertainty, indeterminacy, and liberal states into matroid theory, enhancing its applicability in optimization and combinatorial problems.<br />In the sixth chapter, “Some Graph Parameters for Superhypertree-width and Neutrosophic Tree-width”, the authors discuss graph parameters such as Superhypertree-width and Neutrosophic tree-width. These parameters play a crucial role in the study of graph characteristics, particularly in algorithms and real-world applications. The chapter explores the generalization of hypergraphs to SuperHyperGraphs and examines how these concepts extend tree-width parameters within the context of Neutrosophic logic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8f893643de08f28e03f77369905ae894" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":120060029,"asset_id":126136003,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/120060029/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="126136003"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="126136003"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126136003; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=126136003]").text(description); $(".js-view-count[data-work-id=126136003]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 126136003; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='126136003']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8f893643de08f28e03f77369905ae894" } } $('.js-work-strip[data-work-id=126136003]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":126136003,"title":"Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. 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New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, law, medicine, social science, and some more.<br /><br />This book explores the emerging field of Neutrosophic Algebraic Structures, focusing on both their theoretical foundations and practical applications. We apply innovative algorithmic methods to investigate the complex interactions of neutrosophic elements, such as neutrosophic numbers, sets, and functions, within algebraic systems. Our goal is to show how neutrosophic structures challenge and expand traditional algebraic approaches, offering solutions to problems across diverse fields like computer science, engineering, artificial intelligence, and decision-making.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3d8f1e4643ecaec03cb974b2a6741869" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119975618,"asset_id":126036841,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119975618/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="126036841"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="126036841"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 126036841; 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Anul XV, Nr. 12(172)" class="work-thumbnail" src="https://attachments.academia-assets.com/119939248/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125994017/Constela%C8%9Bii_diamantine_Anul_XV_Nr_12_172_">Constelații diamantine. Anul XV, Nr. 12(172)</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Eseuri, poeme, ilustrații.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a82710567ebf711190db3b4f26ce0953" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119939248,"asset_id":125994017,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119939248/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125994017"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125994017"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125994017; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=125994017]").text(description); $(".js-view-count[data-work-id=125994017]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 125994017; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='125994017']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "a82710567ebf711190db3b4f26ce0953" } } $('.js-work-strip[data-work-id=125994017]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":125994017,"title":"Constelații diamantine. Anul XV, Nr. 12(172)","internal_url":"https://www.academia.edu/125994017/Constela%C8%9Bii_diamantine_Anul_XV_Nr_12_172_","owner_id":4976797,"coauthors_can_edit":true,"owner":{"id":4976797,"first_name":"Florentin","middle_initials":null,"last_name":"Smarandache","page_name":"FlorentinSmarandache","domain_name":"unm","created_at":"2013-07-28T11:35:34.896-07:00","display_name":"Florentin Smarandache","url":"https://unm.academia.edu/FlorentinSmarandache"},"attachments":[{"id":119939248,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/119939248/thumbnails/1.jpg","file_name":"Constelatii_diamantine_nr_172_2024.pdf","download_url":"https://www.academia.edu/attachments/119939248/download_file","bulk_download_file_name":"Constelaii_diamantine_Anul_XV_Nr_12_172.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/119939248/Constelatii_diamantine_nr_172_2024-libre.pdf?1733095212=\u0026response-content-disposition=attachment%3B+filename%3DConstelaii_diamantine_Anul_XV_Nr_12_172.pdf\u0026Expires=1739480826\u0026Signature=UV6RtTxT6sSXnJo59utU6Fjp6iWqcuKP3hj~fQAim3fqjHYIAt6h7hNsqbjky7yPofJDoHrHDrqRS8ON6ybSprKJa7~DGcgZKQ6K75b1bEzQOJXafFeRi-Vb-QwOavy-r3iWmtkPpyBcdARakr3WC14r~Ynu8t8MFGyR2yS3MYXBNjSoC~HmmZdxXV~6AcTOTz~1EMkyq7nYOgsjX5Ex~IOJpjhXB743Br7aSXf1JfQS-xVj2nr6MdUtjpSzXY9S5YT4XBBlVbUVHIBLWOQirNoffPBLV3dD4YVXODruoZg3LvKKxF1K~IqeWCEJPnTIxrm55i8bMn5qpEuPeOKmnA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="125421610"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/125421610/Proceedings_of_the_Mediterranean_Conference_on_Three_Decades_of_Neutrosophic_and_Plithogenic_Theories_and_Applications_MeCoNeT_2024_"><img alt="Research paper thumbnail of Proceedings of the “Mediterranean Conference on Three Decades of Neutrosophic and Plithogenic Theories and Applications” (MeCoNeT 2024)" class="work-thumbnail" src="https://attachments.academia-assets.com/119467965/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125421610/Proceedings_of_the_Mediterranean_Conference_on_Three_Decades_of_Neutrosophic_and_Plithogenic_Theories_and_Applications_MeCoNeT_2024_">Proceedings of the “Mediterranean Conference on Three Decades of Neutrosophic and Plithogenic Theories and Applications” (MeCoNeT 2024)</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This volume contains the proceedings of the Mediterranean Conference on Neutrosophic Theory (MeCo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This volume contains the proceedings of the Mediterranean Conference on Neutrosophic Theory (MeCoNeT 2024), held at the Accademia Peloritana dei Pericolanti of the University of Messina on September 24-25, 2024. The event was organized by the MIFT Department (Mathematics, Computer Science, Physics, and Earth Sciences) of the University of Messina, marking the first international congress on neutrosophic theories outside the Americas. This milestone has firmly established the Mediterranean region as a key hub for research in the rapidly growing field of neutrosophic theory.<br />The MeCoNeT 2024 conference drew over 100 participants from more than 15 countries, with more than 50 scientific contributions selected through a rigorous peer review process. The hybrid format of the event—featuring in-person sessions at the historical Accademia Peloritana dei Pericolanti and online parallel sessions—allowed for broad international participation. The conference thus offered an ideal platform for sharing interdisciplinary research and addressing contemporary challenges in mathematics and beyond.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="32e5a24cc06a56a8aa5dc752445f0827" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119467965,"asset_id":125421610,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119467965/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125421610"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125421610"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125421610; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="125421576"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/125421576/Proceedings_of_the_International_Conference_NeutroGeometry_NeutroAlgebra_and_Their_Applications_Havana_Cuba_12_14_August_2024"><img alt="Research paper thumbnail of Proceedings of the International Conference “NeutroGeometry, NeutroAlgebra, and Their Applications,” Havana, Cuba, 12-14 August 2024" class="work-thumbnail" src="https://attachments.academia-assets.com/119467941/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125421576/Proceedings_of_the_International_Conference_NeutroGeometry_NeutroAlgebra_and_Their_Applications_Havana_Cuba_12_14_August_2024">Proceedings of the International Conference “NeutroGeometry, NeutroAlgebra, and Their Applications,” Havana, Cuba, 12-14 August 2024</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A special issue of the International Journal in Information Science and Engineering “Neutrosophic...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A special issue of the International Journal in Information Science and Engineering “Neutrosophic Sets and Systems” (vol. 71/2024) is dedicated to the Conference on NeutroGeometry, NeutroAlgebra, and Their Applications, organized by the Latin American Association of Neutrosophic Sciences. This event, which took place on August 12-14, 2024, in Havana, Cuba, was made possible by the valuable collaboration of the University of Havana, the University of Physical Culture and Sports Sciences "Manuel Fajardo," the José Antonio Echeverría University of Technology, University of Informatics Sciences and the Cuban Academy of Sciences among other institutions.<br />In 2019 Smarandache generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false} and on 2020 he continued to develop them.<br />The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from our real world. In classical algebraic structures, all operations are 100% well-defined, and all axioms are 100% true, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some operations or some laws.<br />Similarly, a classical Geometry structure has all axioms totally (100%) true. A NeutroGeometry structure has some axioms that are only partially true, and no axiom is totally (100%) false. Whereas an AntiGeometry structure has at least one axiom that is totally (100%) false.<br />And in general, in any field of knowledge one has: Structure, NeutroStructure, and AntiStructure which were inspired from our real world where the laws (axioms) do not equally apply to all people and in the same degree.<br />This special issue aims to highlight the most recent advances and applications in the fields of NeutroGeometry and NeutroAlgebra, two areas that are at the forefront of contemporary mathematical and scientific thought. During the conference, the mathematical foundations and practical applications of these disciplines were explored, as well as their relevance in the MultiAlism system and other interdisciplinary areas. <br />The content of this special issue has been carefully selected to reflect the diversity and depth of the topics discussed at the conference. This event and the subsequent publication of these works underline the growing importance of neutrosophic theories in the current scientific landscape. We are confident that the ideas and discoveries shared in these pages will be of great value to researchers, academics, and professionals interested in these innovative areas of knowledge.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="dcf2555a6c72f3cf7421b0ad3484d3df" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119467941,"asset_id":125421576,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119467941/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125421576"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125421576"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125421576; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="125421526"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/125421526/Proceedings_of_the_International_Conference_on_Neutrosophy_and_Plithogeny_Fundamentals_and_Applications_Lima_Peru_8_9_July_2024"><img alt="Research paper thumbnail of Proceedings of the International Conference on Neutrosophy and Plithogeny: Fundamentals and Applications, Lima, Peru, 8-9 July 2024" class="work-thumbnail" src="https://attachments.academia-assets.com/119467898/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125421526/Proceedings_of_the_International_Conference_on_Neutrosophy_and_Plithogeny_Fundamentals_and_Applications_Lima_Peru_8_9_July_2024">Proceedings of the International Conference on Neutrosophy and Plithogeny: Fundamentals and Applications, Lima, Peru, 8-9 July 2024</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A special issue of the International Journal in Information Science and Engineering “Neutrosophic...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A special issue of the International Journal in Information Science and Engineering “Neutrosophic Sets and Systems” (vol. 69/2024) is dedicated to the Neutrosophic approaches in research, on the occasion of the international and multidisciplinary conference held at the Universidad César Vallejo in Lima, Peru, on July 8 and 9. This event marks a significant milestone, as it is the first time that the Andean region and Latin America host scholars and researchers dedicated to studying various theoretical and applicative issues in the expansive and diverse field of Neutrosophic approaches.<br />Since its conception, Neutrosophic theory has proven to be an interdisciplinary and innovative field, notably growing with the introduction of several generalizations of Neutrosophic Sets, such as Plithogenic Sets, Hypersoft Sets, IndetermSoft Sets, SuperHyperSoft Sets, and MultiAlism. These advanced conceptualizations have further expanded the versatility and application range of Neutrosophic theory, allowing its adoption in an ever-increasing spectrum of disciplines.<br />The conference, with its international and multidisciplinary character, has brought together experts and scholars from various fields, providing a unique platform for the discussion and exchange of ideas on the multiple applications of Neutrosophic approaches. <br />This special issue also addresses how scientific production in Neutrosophy focuses on social issues specific to Latin American philosophy. In the regional context of Latin America, it is possible to state that Neutrosophic tools and knowledge are used for the identification, analysis, and resolution of social problems, offering unique approaches or distinctive contributions to the field of Neutrosophy, influenced by its cultural and philosophical context.<br />Neutrosophic science in Latin America shows a clear pattern of how scientific production addresses social problems, standing out for its innovative approaches that reflect the cultural and philosophical particularities of the region. This approach has allowed Neutrosophy not only to advance in theoretical terms but also to provide practical and contextually relevant solutions to social challenges.<br />This special issue compiles works presented at the conference, reflecting the richness and diversity of current research in this field. We hope that these articles not only contribute to the advancement of knowledge in Neutrosophic theory but also inspire new research and applications in multiple disciplines.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="38879be27925c5934cfdaf9e4f770e09" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119467898,"asset_id":125421526,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119467898/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125421526"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125421526"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125421526; 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Un album de fotografíi din Peru, acompaniat de versurile lui César Vallejo" class="work-thumbnail" src="https://attachments.academia-assets.com/119331804/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125255404/SPeruan%C8%9Ba_Un_album_de_fotograf%C3%ADi_din_Peru_acompaniat_de_versurile_lui_C%C3%A9sar_Vallejo">SPeruanța. Un album de fotografíi din Peru, acompaniat de versurile lui César Vallejo</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated"> Albumul de față conține fotografii din Peru, în special din capitala Lima, capturate în vara anu...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Albumul de față conține fotografii din Peru, în special din capitala Lima, capturate în vara anului 2024, când am vizitat spectaculoasa țară sud-americană cu ocazia unei conferințe științifice pe teme neutrosofice și plitogenice, dar și pentru a-mi vedea pentru prima oară nepoțica tocmai născută, Briana. <br /> Conferința s-a desfășurat la Universidad César Vallejo, Campus los Olivos, în Lima, 8-9 iulie 2024.<br /> Textul care însoțește fotografiile aparțin poetului peruan César Vallejo.<br /> Fotografiile sunt acompaniate de muzică instrumentală produsă de Carlos Carty.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1040cef2a30dae9688657735e9895a36" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119331804,"asset_id":125255404,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119331804/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125255404"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125255404"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125255404; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=125255404]").text(description); $(".js-view-count[data-work-id=125255404]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 125255404; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='125255404']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1040cef2a30dae9688657735e9895a36" } } $('.js-work-strip[data-work-id=125255404]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":125255404,"title":"SPeruanța. 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Some topics introduce new sets such as the Pythagorean neutrosophic vague soft set, the triangular fuzzy penta-partitioned neutrosophic set, interval-valued neutrosophic b-open sets, and interval-valued neutrosophic b-closed sets. Other topics present applications in medical diagnosis, non-preemptive neutrosophic priority queues with uneven services (labeled as NM/NM/1), AHP in an interval neutrosophic set environment, MAGDM in a triangular fuzzy neutrosophic number environment, MAGDM in a pentapartitioned neutrosophic environment, the entropy-ARAS strategy in a single-valued neutrosophic number environment, and the MABAC strategy in a rough neutrosophic set environment.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0478f5d534d83ecf42b15c686675d250" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119331631,"asset_id":125255216,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119331631/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125255216"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125255216"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125255216; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="125255155"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/125255155/Introduction_to_Neutrosophic_Sociology_Neutrosociology_Arabic_translation"><img alt="Research paper thumbnail of Introduction to Neutrosophic Sociology (Neutrosociology). Arabic translation" class="work-thumbnail" src="https://attachments.academia-assets.com/119331584/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125255155/Introduction_to_Neutrosophic_Sociology_Neutrosociology_Arabic_translation">Introduction to Neutrosophic Sociology (Neutrosociology). Arabic translation</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Neutrosophic Sociology (or Neutrosociology) is the study of sociology using neutrosophic scientif...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Neutrosophic Sociology (or Neutrosociology) is the study of sociology using neutrosophic scientific methods. The huge social data that we face in sociology is full of indeterminacy: it is vague, incomplete, contradictory, hybrid, biased, ignorant, redundant, superfluous, meaningless, ambiguous, unclear, etc. That’s why the neutrosophic sciences (which deal with indeterminacy) should be involved, such as: neutrosophy (a new branch of philosophy), neutrosophic set, neutrosophic logic, neutrosophic probability and neutrosophic statistics, neutrosophic analysis, neutrosophic measure, and so on.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7cd86ce25ea61e36289fdcd081d1eb1e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119331584,"asset_id":125255155,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119331584/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125255155"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125255155"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125255155; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=125255155]").text(description); $(".js-view-count[data-work-id=125255155]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 125255155; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='125255155']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7cd86ce25ea61e36289fdcd081d1eb1e" } } $('.js-work-strip[data-work-id=125255155]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":125255155,"title":"Introduction to Neutrosophic Sociology (Neutrosociology). 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Diario fotográfico instantáneo" class="work-thumbnail" src="https://attachments.academia-assets.com/119331535/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125255106/La_Habana_neutros%C3%B3fica_Diario_fotogr%C3%A1fico_instant%C3%A1neo">La Habana, neutrosófica. Diario fotográfico instantáneo</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Este diario fotográfico instantáneo relata, en texto e imágenes, los encuentros científicos y per...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Este diario fotográfico instantáneo relata, en texto e imágenes, los encuentros científicos y personales del autor durante una conferencia de neutrosofía («NeutroÁlgebra y Neutrogeometría con Aplicaciones») celebrada del 12 al 14 de agosto de 2024 en la capital cubana, La Habana, en el Hotel «Habana Libre». El autor ha sido conferenciante invitado en la Comunidad de Inteligencia Artificial para el Desarrollo Sostenible (IADES), así como en el Centro de Investigaciones del Deporte Cubano (CIDC) o en el Joven Club de Computación y Electrónica, donando numerosos libros científicos a bibliotecas de La Habana y concediendo entrevistas a publicaciones cubanas.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="27425444ecc90003cbed769bd277745c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":119331535,"asset_id":125255106,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/119331535/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="125255106"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="125255106"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 125255106; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=125255106]").text(description); $(".js-view-count[data-work-id=125255106]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 125255106; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='125255106']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "27425444ecc90003cbed769bd277745c" } } $('.js-work-strip[data-work-id=125255106]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":125255106,"title":"La Habana, neutrosófica. 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Fotojurnal instantaneu</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Acest fotojurnal instantaneu relatează o vizită în Peru, dublu ocazionată: o conferință științifi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Acest fotojurnal instantaneu relatează o vizită în Peru, dublu ocazionată: o conferință științifică pe teme de neutrosofie la care profesorul Smarandache a participat la Lima și vizitarea primei (tocmai) născute nepoate a autorului. Ca în fiecare jurnal al său de călătorie, autorul nu scapă prilejul de a observa viața reală din locul vizitat și de a recapitula, expeditiv, date istorice, științifice sau naturale. 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Fotojurnal instantaneu" class="work-thumbnail" src="https://attachments.academia-assets.com/119331477/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/125255030/Havana_neutrosofic%C4%83_Fotojurnal_instantaneu">Havana, neutrosofică. Fotojurnal instantaneu</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Fotojurnalul de față relatează, în text și imagini, întâlniri științifice și personale ale autoru...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Fotojurnalul de față relatează, în text și imagini, întâlniri științifice și personale ale autorului ocazionate de o conferință de neutrosofie (“NeutroAlgebră și NeutroGeometrie cu aplicații”) desfășurată între 12 și 14 august 2024, în capitala Cubei, Havana, la Hotelul “Habana Libre”. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="11166968"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/11166968/%CE%B1_Discounting_Method_for_Multi_Criteria_Decision_Making_%CE%B1_D_MCDM_"><img alt="Research paper thumbnail of α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM)" class="work-thumbnail" src="https://attachments.academia-assets.com/36807702/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/11166968/%CE%B1_Discounting_Method_for_Multi_Criteria_Decision_Making_%CE%B1_D_MCDM_">α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM)</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MumtazAli22">Mumtaz Ali</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://unm.academia.edu/FlorentinSmarandache">Florentin Smarandache</a></span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this book we introduce a new procedure called α-Discounting Method for Multi-Criteria Decision...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this book we introduce a new procedure called α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-DMCDM is afterwards generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or non-homogeneous equations and/or inequalities.<br />The general idea of α-D MCDM is to assign non-null positive parameters<br />α1, α2, …, αp to the coefficients in the right-hand side of each preference that diminish or increase them in order to transform the above linear homogeneous system of equations which has only the null-solution, into a system having a particular non-null solution. After finding the general<br />solution of this system, the principles used to assign particular values to all parameters α’s is the second important part of α-D, yet to be deeper investigated in the future.<br />In the current book we propose the Fairness Principle, i.e. each<br />coefficient should be discounted with the same percentage (we think this is<br />fair: not making any favoritism or unfairness to any coefficient), but the<br />reader can propose other principles.<br />For consistent decision-making problems with pairwise comparisons, α-<br />Discounting Method together with the Fairness Principle give the same<br />result as AHP.<br />But for weak inconsistent decision-making problem, α-Discounting together with the Fairness Principle give a different result from AHP. Many consistent, weak inconsistent, and strong inconsistent examplesare given in this book.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="54eda2c891d0ca92d358816770e581d4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":36807702,"asset_id":11166968,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/36807702/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="11166968"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="11166968"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 11166968; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="5975912" id="conferencepresentations"><div class="js-work-strip profile--work_container" data-work-id="41125450"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/41125450/Neutrosophic_Set_is_a_Generalization_of_Intuitionistic_Fuzzy_Set_Picture_Fuzzy_Set_Pythagorean_Fuzzy_Set_q_Rung_Orthopair_Fuzzy_Set_Spherical_Fuzzy_Set_and_n_HyperSpherical_Fuzzy_Set_while_Neutrosophication_is_a_Generalization_of_Regret_Theory_Grey_System_Theory_and_Three_Ways_Decision"><img alt="Research paper thumbnail of Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Picture Fuzzy Set, Pythagorean Fuzzy Set, q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, and n-HyperSpherical Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision" class="work-thumbnail" src="https://attachments.academia-assets.com/61378113/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/41125450/Neutrosophic_Set_is_a_Generalization_of_Intuitionistic_Fuzzy_Set_Picture_Fuzzy_Set_Pythagorean_Fuzzy_Set_q_Rung_Orthopair_Fuzzy_Set_Spherical_Fuzzy_Set_and_n_HyperSpherical_Fuzzy_Set_while_Neutrosophication_is_a_Generalization_of_Regret_Theory_Grey_System_Theory_and_Three_Ways_Decision">Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Picture Fuzzy Set, Pythagorean Fuzzy Set, q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, and n-HyperSpherical Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision</a></div><div class="wp-workCard_item"><span>Journal of Number Theory</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IF...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembership are taken. NS is also more flexible and effective because it handles, besides independent components, also partially independent and partially dependent components, while IFS cannot deal with these.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="31d13401e36d87869cfb20034962123e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":61378113,"asset_id":41125450,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/61378113/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="41125450"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="41125450"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 41125450; 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Nonetheless, we are aware that this article sounds quite gloomy.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="dcd46b8b26f6e111db3cdf79223d4a45" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":57244485,"asset_id":37289369,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/57244485/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="37289369"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="37289369"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 37289369; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="34679970"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/34679970/Neutrosophy_Method_of_Uncertainties_Process_Analysis"><img alt="Research paper thumbnail of Neutrosophy, Method of Uncertainties Process Analysis" class="work-thumbnail" src="https://attachments.academia-assets.com/54539155/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/34679970/Neutrosophy_Method_of_Uncertainties_Process_Analysis">Neutrosophy, Method of Uncertainties Process Analysis</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper presents the importance of Neutrosophy theory in order to find a method that could sol...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper presents the importance of Neutrosophy theory in order to find a method that could solve the uncertainties arising on manufacturing process. The aim of this pilot study is to find a procedure to diminish the uncertainties induced by manufacturing, maintenance,<br />logistics, design, human resources. The study is intended to identify a method to answer uncertainties solving in order to support manufacturing managers, artificial intelligence researchers and businessman in general.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a4bd2a3f3949cb265873e1a495023403" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":54539155,"asset_id":34679970,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/54539155/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="34679970"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="34679970"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 34679970; 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(abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/49802642/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/29359914/What_Happens_to_the_Curved_Space_around_a_Massive_Object_that_has_been_Destroyed_abstract_">What Happens to the Curved Space around a Massive Object that has been Destroyed? (abstract)</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated"> According to the General Theory of Relativity the space is curved around a massive object. Then,...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">According to the General Theory of Relativity the space is curved around a massive object. 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(abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/49802554/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/29359761/Open_question_What_is_the_Maximum_Chain_Length_of_Orbiting_Bodies_abstract_">Open question: What is the Maximum Chain Length of Orbiting Bodies? (abstract)</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In the macrocosmos, let’s consider an astronomical body (A1), around which orbits another astrono...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In the macrocosmos, let’s consider an astronomical body (A1), around which orbits another astronomical body (A2), and around (A2) orbits another astronomical body (A3), and again around (A3) orbits another astronomical body (A4), and so on.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e4356152cf98084a2089cf58db347571" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":49802554,"asset_id":29359761,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/49802554/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="29359761"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="29359761"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 29359761; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=29359761]").text(description); $(".js-view-count[data-work-id=29359761]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 29359761; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='29359761']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e4356152cf98084a2089cf58db347571" } } $('.js-work-strip[data-work-id=29359761]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":29359761,"title":"Open question: What is the Maximum Chain Length of Orbiting Bodies? 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="29359742"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/29359742/Numerical_Solution_of_Quantum_Cosmological_Model_Simulating_Boson_and_Fermion_Creation_abstract_"><img alt="Research paper thumbnail of Numerical Solution of Quantum Cosmological Model Simulating Boson and Fermion Creation (abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/49802513/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/29359742/Numerical_Solution_of_Quantum_Cosmological_Model_Simulating_Boson_and_Fermion_Creation_abstract_">Numerical Solution of Quantum Cosmological Model Simulating Boson and Fermion Creation (abstract)</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boso...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="50466887328ab4a0b44b02187f704fff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":49802513,"asset_id":29359742,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/49802513/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="29359742"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="29359742"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 29359742; 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its reference is the sun, and its speed is limited to less than the speed of light, c, relative to the sun.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="53d92af023395839437b214bb6d7c1d5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":49802464,"asset_id":29359703,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/49802464/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="29359703"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="29359703"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 29359703; 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