Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems | Journal of Computational and Cognitive Engineering

<!DOCTYPE html> <html lang="en" xml:lang="en"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title> Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems | Journal of Computational and Cognitive Engineering </title> <link rel="icon" href="https://ojs.bonviewpress.com/public/journals/4/favicon_en_US.png"> <meta name="generator" content="Open Journal Systems 3.4.0.7"> <meta name="gs_meta_revision" content="1.1"/> <meta name="citation_journal_title" content="Journal of Computational and Cognitive Engineering"/> <meta name="citation_journal_abbrev" content="JCCE"/> <meta name="citation_issn" content="2810-9503"/> <meta name="citation_author" content="Arun Sarkar"/> <meta name="citation_author_institution" content="Department of Mathematics, Heramba Chandra College, India"/> <meta name="citation_author" content="Animesh Biswas"/> <meta name="citation_author_institution" content="Department of Mathematics, University of Kalyani, India"/> <meta name="citation_author" content="Moitreyee Kundu"/> <meta name="citation_author_institution" content="Department of Mathematics, University of Kalyani, India"/> <meta name="citation_title" content="Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems"/> <meta name="citation_language" content="en"/> <meta name="citation_date" content="2022/04/12"/> <meta name="citation_volume" content="1"/> <meta name="citation_issue" content="3"/> <meta name="citation_firstpage" content="109"/> <meta name="citation_lastpage" content="121"/> <meta name="citation_doi" content="10.47852/bonviewJCCE2202162"/> <meta name="citation_abstract_html_url" content="https://ojs.bonviewpress.com/index.php/JCCE/article/view/162"/> <meta name="citation_abstract" xml:lang="en" content="Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. The purpose of this study is to explore the multicriteria group decision-making (MCGDM) problem with the q-rung orthopair trapezoidal fuzzy (q-ROTrF) context by employing Einstein t-conorms and t-norms. Firstly, some arithmetical operations for q-ROTrF numbers, such as Einstein-based sum, product, scalar multiplication, and exponentiation, are introduced based on Einstein t-conorms and t-norms. Then, Einstein operations-based averaging and geometric aggregation operators (AOs), viz., q-ROTrF Einstein weighted averaging and weighted geometric operators, are developed. Further, some prominent characteristics of the suggested operators are investigated. Then, based on defined AOs, a MCGDM model with q-ROTrF numbers is developed. In accordance with the proposed operators and the developed model, two numerical examples are illustrated. The impacts of the rung parameter on decision results are also analyzed in detail to reflect the suitability and supremacy of the developed approach. 聽 Received: 25 January 2022 | Revised: 30 March 2022 | Accepted: 11 April 2022 聽 Conflicts of Interest The authors declare that they have no conflicts of interest to this work."/> <meta name="citation_keywords" xml:lang="en" content="multicriteria group decision-making"/> <meta name="citation_keywords" xml:lang="en" content="q-rung orthopair trapezoidal fuzzy number"/> <meta name="citation_keywords" xml:lang="en" content="Einstein operations"/> <meta name="citation_keywords" xml:lang="en" content="weighted averaging and weighted geometric aggregating operators"/> <meta name="citation_pdf_url" content="https://ojs.bonviewpress.com/index.php/JCCE/article/download/162/126"/> <link rel="schema.DC" href="http://purl.org/dc/elements/1.1/" /> <meta name="DC.Creator.PersonalName" content="Arun Sarkar"/> <meta name="DC.Creator.PersonalName" content="Animesh Biswas"/> <meta name="DC.Creator.PersonalName" content="Moitreyee Kundu"/> <meta name="DC.Date.created" scheme="ISO8601" content="2022-04-12"/> <meta name="DC.Date.dateSubmitted" scheme="ISO8601" content="2022-01-24"/> <meta name="DC.Date.issued" scheme="ISO8601" content="2022-08-08"/> <meta name="DC.Date.modified" scheme="ISO8601" content="2024-01-10"/> <meta name="DC.Description" xml:lang="en" content="Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. The purpose of this study is to explore the multicriteria group decision-making (MCGDM) problem with the q-rung orthopair trapezoidal fuzzy (q-ROTrF) context by employing Einstein t-conorms and t-norms. Firstly, some arithmetical operations for q-ROTrF numbers, such as Einstein-based sum, product, scalar multiplication, and exponentiation, are introduced based on Einstein t-conorms and t-norms. Then, Einstein operations-based averaging and geometric aggregation operators (AOs), viz., q-ROTrF Einstein weighted averaging and weighted geometric operators, are developed. Further, some prominent characteristics of the suggested operators are investigated. Then, based on defined AOs, a MCGDM model with q-ROTrF numbers is developed. In accordance with the proposed operators and the developed model, two numerical examples are illustrated. The impacts of the rung parameter on decision results are also analyzed in detail to reflect the suitability and supremacy of the developed approach. 聽 Received: 25 January 2022 | Revised: 30 March 2022 | Accepted: 11 April 2022 聽 Conflicts of Interest The authors declare that they have no conflicts of interest to this work."/> <meta name="DC.Format" scheme="IMT" content="application/pdf"/> <meta name="DC.Identifier" content="162"/> <meta name="DC.Identifier.pageNumber" content="109-121"/> <meta name="DC.Identifier.DOI" content="10.47852/bonviewJCCE2202162"/> <meta name="DC.Identifier.URI" content="https://ojs.bonviewpress.com/index.php/JCCE/article/view/162"/> <meta name="DC.Language" scheme="ISO639-1" content="en"/> <meta name="DC.Rights" content="Copyright (c) 2022 Authors"/> <meta name="DC.Rights" content="https://creativecommons.org/licenses/by/4.0/"/> <meta name="DC.Source" content="Journal of Computational and Cognitive Engineering"/> <meta name="DC.Source.ISSN" 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class="page_title"> Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems </h1> <div class="row"> <div class="main_entry"> <section class="item authors"> <h2 class="pkp_screen_reader">Authors</h2> <ul class="authors"> <li> <span class="name"> Arun Sarkar </span> <span class="affiliation"> Department of Mathematics, Heramba Chandra College, India </span> </li> <li> <span class="name"> Animesh Biswas </span> <span class="affiliation"> Department of Mathematics, University of Kalyani, India </span> </li> <li> <span class="name"> Moitreyee Kundu </span> <span class="affiliation"> Department of Mathematics, University of Kalyani, India </span> </li> </ul> </section> <section class="item doi"> <h2 class="label"> DOI: </h2> <span class="value"> <a href="https://doi.org/10.47852/bonviewJCCE2202162"> https://doi.org/10.47852/bonviewJCCE2202162 </a> </span> </section> <section class="item keywords"> <h2 class="label"> Keywords: </h2> <span class="value"> multicriteria group decision-making, q-rung orthopair trapezoidal fuzzy number, Einstein operations, weighted averaging and weighted geometric aggregating operators </span> </section> <section class="item abstract"> <h2 class="label">Abstract</h2> <p>Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. The purpose of this study is to explore the multicriteria group decision-making (MCGDM) problem with the q-rung orthopair trapezoidal fuzzy (q-ROTrF) context by employing Einstein t-conorms and t-norms. Firstly, some arithmetical operations for q-ROTrF numbers, such as Einstein-based sum, product, scalar multiplication, and exponentiation, are introduced based on Einstein t-conorms and t-norms. Then, Einstein operations-based averaging and geometric aggregation operators (AOs), viz., q-ROTrF Einstein weighted averaging and weighted geometric operators, are developed. Further, some prominent characteristics of the suggested operators are investigated. Then, based on defined AOs, a MCGDM model with q-ROTrF numbers is developed. In accordance with the proposed operators and the developed model, two numerical examples are illustrated. The impacts of the rung parameter on decision results are also analyzed in detail to reflect the suitability and supremacy of the developed approach.</p> <p>聽</p> <p><strong>Received</strong>: 25 January 2022 | <strong>Revised</strong>: 30 March 2022 | <strong>Accepted</strong>: 11 April 2022</p> <p>聽</p> <p><strong>Conflicts of Interest</strong></p> <p>The authors declare that they have no conflicts of interest to this work.</p> </section> <br /><div class="separator"></div><div class="item abstract" id="trendmd-suggestions"></div><script defer src='//js.trendmd.com/trendmd.min.js' data-trendmdconfig='{"website_id":"89267", "element":"#trendmd-suggestions"}'></script><div class="item downloads_chart"> <h3 class="label"> Metrics </h3> <div id="paperbuzz"><div id="loading">Metrics Loading ...</div></div> <script type="text/javascript"> window.onload = function () { var options = { paperbuzzStatsJson: JSON.parse('{\"altmetrics_sources\":[{\"events\":null,\"events_count\":338,\"events_count_by_day\":[{\"count\":\"5\",\"date\":\"2022-04-12\"},{\"count\":\"3\",\"date\":\"2022-04-13\"},{\"count\":\"4\",\"date\":\"2022-04-14\"},{\"count\":\"1\",\"date\":\"2022-04-15\"},{\"count\":\"4\",\"date\":\"2022-04-19\"},{\"count\":\"4\",\"date\":\"2022-04-20\"},{\"count\":\"1\",\"date\":\"2022-04-21\"},{\"count\":\"3\",\"date\":\"2022-04-22\"},{\"count\":\"1\",\"date\":\"2022-04-24\"},{\"count\":\"2\",\"date\":\"2022-04-25\"},{\"count\":\"11\",\"date\":\"2022-04-29\"},{\"count\":\"4\",\"date\":\"2022-04-30\"},{\"count\":\"1\",\"date\":\"2022-05-02\"},{\"count\":\"1\",\"date\":\"2022-05-03\"},{\"count\":\"3\",\"date\":\"2022-05-07\"},{\"count\":\"1\",\"date\":\"2022-05-10\"},{\"count\":\"2\",\"date\":\"2022-05-12\"}],\"events_count_by_month\":[{\"count\":\"43\",\"date\":\"2022-04\"},{\"count\":\"14\",\"date\":\"2022-05\"},{\"count\":\"12\",\"date\":\"2022-06\"},{\"count\":\"8\",\"date\":\"2022-07\"},{\"count\":\"24\",\"date\":\"2022-08\"},{\"count\":\"17\",\"date\":\"2022-09\"},{\"count\":\"15\",\"date\":\"2022-10\"},{\"count\":\"9\",\"date\":\"2022-11\"},{\"count\":\"9\",\"date\":\"2022-12\"},{\"count\":\"4\",\"date\":\"2023-01\"},{\"count\":\"4\",\"date\":\"2023-02\"},{\"count\":\"2\",\"date\":\"2023-03\"},{\"count\":\"6\",\"date\":\"2023-04\"},{\"count\":\"14\",\"date\":\"2023-05\"},{\"count\":\"12\",\"date\":\"2023-06\"},{\"count\":\"8\",\"date\":\"2023-07\"},{\"count\":\"6\",\"date\":\"2023-08\"},{\"count\":\"8\",\"date\":\"2023-09\"},{\"count\":\"12\",\"date\":\"2023-10\"},{\"count\":\"4\",\"date\":\"2023-11\"},{\"count\":\"10\",\"date\":\"2023-12\"},{\"count\":\"8\",\"date\":\"2024-01\"},{\"count\":\"4\",\"date\":\"2024-02\"},{\"count\":\"6\",\"date\":\"2024-03\"},{\"count\":\"9\",\"date\":\"2024-04\"},{\"count\":\"6\",\"date\":\"2024-05\"},{\"count\":\"18\",\"date\":\"2024-06\"},{\"count\":\"3\",\"date\":\"2024-07\"},{\"count\":\"18\",\"date\":\"2024-08\"},{\"count\":\"14\",\"date\":\"2024-09\"},{\"count\":\"9\",\"date\":\"2024-10\"},{\"count\":\"2\",\"date\":\"2024-11\"}],\"events_count_by_year\":[{\"count\":\"151\",\"date\":\"2022\"},{\"count\":\"90\",\"date\":\"2023\"},{\"count\":\"97\",\"date\":\"2024\"}],\"source\":{\"display_name\":\"File downloads\"},\"source_id\":\"fileDownloads\"}],\"crossref_event_data_url\":\"https:\\/\\/api.eventdata.crossref.org\\/v1\\/events?rows=1000&filter=from-collected-date:1990-01-01,until-collected-date:2099-01-01,obj-id:10.47852\\/bonviewjcce2202162\",\"doi\":\"10.47852\\/bonviewjcce2202162\",\"metadata\":{\"DOI\":\"10.47852\\/bonviewjcce2202162\",\"ISSN\":[\"2810-9503\"],\"URL\":\"http:\\/\\/dx.doi.org\\/10.47852\\/bonviewjcce2202162\",\"abstract\":\"<jats:p>Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. 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Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems | Journal of Computational and Cognitive Engineering