Two Novel Generalized Information Measures for Fuzzy Sets

<!DOCTYPE html>    <html>  <head> <meta charset="utf-8" /> <title>Two Novel Generalized Information Measures for Fuzzy Sets</title>  <link rel="shortcut icon" type="image/ico" href="./data/ijsom/coversheet/favicon.ico" />  <meta name="viewport" content="width=device-width, maximum-scale=1, initial-scale=1, user-scalable=0" />   <meta name="keywords" content="Fuzzy Set,Fuzzy Entropy,Membership Function,measure,Vagueness" /> <meta name="description" content="In the present manuscript, it is our utmost aim and objective to comprehensively and extensively expound upon two highly innovative and remarkably novel information measures that have been adeptly and appropriately extended to encompass fuzzy sets. These measures have undergone a rigorous and meticulous scrutiny and examination with regard to axiomatic principles, and have evinced numerous and manifold advantageous properties, thus providing a compelling and highly persuasive validation of their reliability, credibility, and overall effectiveness. It is of paramount importance to note that the measures in question have been meticulously and painstakingly designed with the express aim and purpose of effectively quantifying the extent of information that is inextricably embedded and enmeshed within fuzzy sets, and are firmly grounded in the foundational and bedrock principles of information theory, which is an indisputably and irrefutably significant and substantial academic discipline. Our contributions to the field of study are truly and incontestably unparalleled, and offer a fresh, innovative, and unprecedented perspective on the study of fuzzy sets and their associated information content, which is of immense and inestimable value to the overall advancement and progress of the academic discipline." /> <meta name="title" content="Two Novel Generalized Information Measures for Fuzzy Sets" /> <meta name="googlebot" content="NOODP" /> <meta name="citation_title" content="Two Novel Generalized Information Measures for Fuzzy Sets" /> <meta name="citation_author" content="Kumar, Ashok" /> <meta name="citation_author_institution" content="Applied Sciences, Faculty, Chitkara University, Himachal Pradesh, India" /> <meta name="citation_author" content="Kumar, Krishan" /> <meta name="citation_author_institution" content="Deen Bandhu Chhotu Ram University of Science and Technology, Haryana-131039, India" /> <meta name="citation_author" content="Gupta, Madhu" /> <meta name="citation_author_institution" content="Chitkara University School of Engineering and Technology, Chitkara University, Himachal Pradesh, India" /> <meta name="citation_author" content="Deswal, Komal Kumari" /> <meta name="citation_author_institution" content="Atal Shiksha Kunj, Atal Nagar, Barotiwala, Solan, Himachal Pradesh" /> <meta name="citation_author" content="Das, Bhagwan" /> <meta name="citation_author_institution" content="Government College Haryana-126102, India" /> <meta name="citation_abstract" content="In the present manuscript, it is our utmost aim and objective to comprehensively and extensively expound upon two highly innovative and remarkably novel information measures that have been adeptly and appropriately extended to encompass fuzzy sets. These measures have undergone a rigorous and meticulous scrutiny and examination with regard to axiomatic principles, and have evinced numerous and manifold advantageous properties, thus providing a compelling and highly persuasive validation of their reliability, credibility, and overall effectiveness. It is of paramount importance to note that the measures in question have been meticulously and painstakingly designed with the express aim and purpose of effectively quantifying the extent of information that is inextricably embedded and enmeshed within fuzzy sets, and are firmly grounded in the foundational and bedrock principles of information theory, which is an indisputably and irrefutably significant and substantial academic discipline. Our contributions to the field of study are truly and incontestably unparalleled, and offer a fresh, innovative, and unprecedented perspective on the study of fuzzy sets and their associated information content, which is of immense and inestimable value to the overall advancement and progress of the academic discipline." /> <meta name="citation_id" content="2921" /> <meta name="citation_publication_date" content="2024/02/01" /> <meta name="citation_date" content="2024-02-01" /> <meta name="citation_journal_title" content="International Journal of Supply and Operations Management" /> <meta name="citation_issn" content="23831359" /> <meta name="citation_volume" content="11" /> <meta name="citation_issue" content="1" /> <meta name="citation_firstpage" content="43" /> <meta name="citation_lastpage" content="53" /> <meta name="citation_publisher" content="Kharazmi University" /> <meta name="citation_doi" content="10.22034/ijsom.2023.109243.2271" /> <meta name="DC.Identifier" content="10.22034/ijsom.2023.109243.2271" /> <meta name="citation_abstract_html_url" content="http://www.ijsom.com/article_2921.html" /> <meta name="citation_pdf_url" content="http://www.ijsom.com/article_2921_c58a6e2e2c775e2a27247f16a9b1fd1c.pdf" /> <meta name="DC.Title" content="Two Novel Generalized Information Measures for Fuzzy Sets" /> <meta name="DC.Source" content="International Journal of Supply and Operations Management" /> <meta name="DC.Date" content="01/02/2024" /> <meta name="DC.Date.issued" content="2024-02-01" /> <meta name="DC.Format" content="application/pdf" /> <meta name="DC.Contributor" content="Kumar, Ashok" /> <meta name="DC.Contributor" content="Kumar, Krishan" /> <meta name="DC.Contributor" content="Gupta, Madhu" /> <meta name="DC.Contributor" content="Deswal, Komal Kumari" /> <meta name="DC.Contributor" content="Das, Bhagwan" /> <meta name="og:title" content="Two Novel Generalized Information Measures for Fuzzy Sets" /> <meta name="og:description" content="In the present manuscript, it is our utmost aim and objective to comprehensively and extensively expound upon two highly innovative and remarkably novel information measures that have been adeptly and appropriately extended to encompass fuzzy sets. These measures have undergone a rigorous and meticulous scrutiny and examination with regard to axiomatic principles, and have evinced numerous and manifold advantageous properties, thus providing a compelling and highly persuasive validation of their reliability, credibility, and overall effectiveness. It is of paramount importance to note that the measures in question have been meticulously and painstakingly designed with the express aim and purpose of effectively quantifying the extent of information that is inextricably embedded and enmeshed within fuzzy sets, and are firmly grounded in the foundational and bedrock principles of information theory, which is an indisputably and irrefutably significant and substantial academic discipline. 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Type : Research Paper</p> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Authors</strong></p> <ul class="list-inline list-inline-seprator margin-bottom-6 ltr"> <li class="padding-3"> <a href="./?_action=article&au=125885&_au=Ashok++Kumar">Ashok Kumar</a> <sup class="ltr"><a class=" text-green" href="https://www.orcid.org/000000024299626X" data-toggle="tooltip" data-placement="bottom" data-html="true" title="ORCID: 000000024299626X" target="_blank"><i class="ai ai-orcid size-13" ></i></a></sup> <sup><a href="#aff1" >1</a></sup> </li> <li class="padding-3"> <a href="./?_action=article&au=125918&_au=Krishan++Kumar">Krishan Kumar</a> <sup><a href="mailto:dahiya_krishan@rediffmail.com" data-toggle="tooltip" data-placement="bottom" title="Email to Corresponding Author"><i class="fa fa-envelope-o" ></i></a></sup> <sup><a href="#aff2" >2</a></sup> </li> <li class="padding-3"> <a href="./?_action=article&au=125902&_au=Madhu++Gupta">Madhu Gupta</a> <sup class="ltr"><a class=" text-green" href="https://www.orcid.org/0000000150622199" data-toggle="tooltip" data-placement="bottom" data-html="true" title="ORCID: 0000000150622199" target="_blank"><i class="ai ai-orcid size-13" ></i></a></sup> <sup><a href="#aff3" >3</a></sup> </li> <li class="padding-3"> <a href="./?_action=article&au=125919&_au=Komal+Kumari+Deswal">Komal Kumari Deswal</a> <sup><a href="#aff4" >4</a></sup> </li> <li class="padding-3"> <a href="./?_action=article&au=125920&_au=Bhagwan++Das">Bhagwan Das</a> <sup><a href="#aff5" >5</a></sup> </li> </ul> <p class="margin-bottom-3 ltr" id="aff1"> <sup>1</sup> Applied Sciences, Faculty, Chitkara University, Himachal Pradesh, India </p> <p class="margin-bottom-3 ltr" id="aff2"> <sup>2</sup> Deen Bandhu Chhotu Ram University of Science and Technology, Haryana-131039, India </p> <p class="margin-bottom-3 ltr" id="aff3"> <sup>3</sup> Chitkara University School of Engineering and Technology, Chitkara University, Himachal Pradesh, India </p> <p class="margin-bottom-3 ltr" id="aff4"> <sup>4</sup> Atal Shiksha Kunj, Atal Nagar, Barotiwala, Solan, Himachal Pradesh </p> <p class="margin-bottom-3 ltr" id="aff5"> <sup>5</sup> Government College Haryana-126102, India </p> <div class="margin-bottom-3 ltr" id="ar_doi" title="DOI"><i class="ai ai-doi size-25 text-orange"></i> <span dir="ltr"><a href="https://dx.doi.org/10.22034/ijsom.2023.109243.2271">10.22034/ijsom.2023.109243.2271</a></span></div> <p style="margin:12px -2px 0 -2px"><strong>Abstract</strong></p> <div class="padding_abstract justify ltr">In the present manuscript, it is our utmost aim and objective to comprehensively and extensively expound upon two highly innovative and remarkably novel information measures that have been adeptly and appropriately extended to encompass fuzzy sets. These measures have undergone a rigorous and meticulous scrutiny and examination with regard to axiomatic principles, and have evinced numerous and manifold advantageous properties, thus providing a compelling and highly persuasive validation of their reliability, credibility, and overall effectiveness. It is of paramount importance to note that the measures in question have been meticulously and painstakingly designed with the express aim and purpose of effectively quantifying the extent of information that is inextricably embedded and enmeshed within fuzzy sets, and are firmly grounded in the foundational and bedrock principles of information theory, which is an indisputably and irrefutably significant and substantial academic discipline. Our contributions to the field of study are truly and incontestably unparalleled, and offer a fresh, innovative, and unprecedented perspective on the study of fuzzy sets and their associated information content, which is of immense and inestimable value to the overall advancement and progress of the academic discipline.</div> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Keywords</strong></p> <ul class="block list-inline list-inline-seprator margin-bottom-6 ltr"> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=106454&_kw=Fuzzy+Set" >Fuzzy Set</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=106455&_kw=Fuzzy+Entropy" >Fuzzy Entropy</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=106456&_kw=Membership+Function" >Membership Function</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=6022&_kw=Measure" >Measure</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=106458&_kw=Vagueness" >Vagueness</a> </li> </ul> </div> <hr> <div class="page_break"></div> <div class="panel"> <div class="panel-heading card-header"> <h4 class="panel-title "> <a data-toggle="collapse" data-parent="#accordions" href="#collapsesRef"><i class="fa fa-plus"></i> References</a> </h4> </div> <div id="collapsesRef" class="panel-collapse collapse"> <div class="panel-body justify"> <div class="padding-3 margin-top-3 ltr justify">Bhandari, D., and Pal, N. 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New picture fuzzy entropy in regarding to multi-criteria decision-making application<em>.</em> <em>AIP Conference Proceedings, 2357</em> (1). AIP Publishing. </div> <div class="padding-3 margin-top-3 ltr justify">Tomar, V. P., and Ohlan, A. (2014). Two new parametric generalized R-norm fuzzy information measures<em>.</em> <em>International Journal of Computer Applications, 93</em>(13), 22-27. </div> <div class="padding-3 margin-top-3 ltr justify">Tomar, V. P., and Ohlan, A. (2014). Sequence of fuzzy divergence measures and inequalities. <em>AMO - Advanced Modeling and Optimization, 16</em>(2), 439-452. </div> <div class="padding-3 margin-top-3 ltr justify">Tomar, V. P., and Ohlan, A. (2014). Sequence of inequalities among fuzzy mean difference divergence measures and their applications, <em>SpringerPlus, 3</em>, 623, 1-20. </div> <div class="padding-3 margin-top-3 ltr justify">Tomar, V. P., and Ohlan, A. (2014). New parametric generalized exponential fuzzy divergence measure. <em>Journal of Uncertainty Analysis and Applications, 2</em>(1), 1-14. </div> <div class="padding-3 margin-top-3 ltr justify">Tomar, V. P., and Ohlan, A. (2015). A new generalized fuzzy divergence measure and applications. <em>Fuzzy Information and Engineering, 7</em>(4), 507-523. </div> <div class="padding-3 margin-top-3 ltr justify">Verma, R., and Merigó, J.M. (2019). On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision鈥恗aking. <em>International Journal of Intelligent Systems, 34</em>(10), 2556-2583. </div> <div class="padding-3 margin-top-3 ltr justify">Verma, R., and Sharma, B. D. (2011). On Generalized Exponential Fuzzy Entropy. <em>World Academy of Science, Engineering and Technology, 60</em>, 1402-1405.            </div> <div class="padding-3 margin-top-3 ltr justify">Zadeh, L. A. (1968). 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Fuzzy Sets. <em>Information and Control, 8</em>, 338-353.</div> </div> </div> </div> </div> </div>   <div class="col-lg-3 col-md-3 col-sm-4"> <div class="panel panel-default my_panel-default margin-bottom-10"> <div class="panel-body ar_info_pnl" id="ar_info_pnl_cover"> <div id="pnl_cover"> <div class="row" > <div class="col-xs-6 col-md-6 nomargin-bottom"> <a href="javascript:loadModal('International Journal of Supply and Operations Management', './data/ijsom/coversheet/cover_en.jpg')"> <img src="data/ijsom/coversheet/cover_en.jpg" alt="International Journal of Supply and Operations Management" style="width: 100%;"> </a> </div> <div class="col-xs-6 col-md-6 nomargin-bottom"> <h6><a href="./issue_542_543.html">Volume 11, Issue 1</a><br/>February 2024<div id="sp_ar_pages">Pages <span dir="ltr">43-53</span></div></h6> </div> </div> </div> </div> </div>  <div class="panel panel-default my_panel-default margin-bottom-10 panel-lists"> <div class="panel-heading"> <h3 class="panel-title"><a 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class="list-group-item"><a class="tag_a">PDF Download: <i>220</i></a></li> </ul> </div> </div> </div> </div>  </div> </section> <div id="cite-apa" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content">  <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">APA</h4> </div>  <div class="modal-body"> <p>Kumar, A., Kumar, K., Gupta, M., Deswal, K., & Das, B. (2024). Two Novel Generalized Information Measures for Fuzzy Sets. <em>International Journal of Supply and Operations Management</em>, 11(1), 43-53. doi: 10.22034/ijsom.2023.109243.2271</p> </div> </div> </div> </div> <div id="cite-mla" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content">  <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">MLA</h4> </div>  <div class="modal-body"> <p>Ashok Kumar; Krishan Kumar; Madhu Gupta; Komal Kumari Deswal; Bhagwan Das. "Two Novel Generalized Information Measures for Fuzzy Sets". <em>International Journal of Supply and Operations Management</em>, 11, 1, 2024, 43-53. doi: 10.22034/ijsom.2023.109243.2271</p> </div> </div> </div> </div> <div id="cite-harvard" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content">  <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">HARVARD</h4> </div>  <div class="modal-body"> <p>Kumar, A., Kumar, K., Gupta, M., Deswal, K., Das, B. (2024). 'Two Novel Generalized Information Measures for Fuzzy Sets', <em>International Journal of Supply and Operations Management</em>, 11(1), pp. 43-53. doi: 10.22034/ijsom.2023.109243.2271</p> </div> </div> </div> </div> <div id="cite-vancouver" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content">  <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">VANCOUVER</h4> </div>  <div class="modal-body"> <p>Kumar, A., Kumar, K., Gupta, M., Deswal, K., Das, B. Two Novel Generalized Information Measures for Fuzzy Sets. <em>International Journal of Supply and Operations Management</em>, 2024; 11(1): 43-53. doi: 10.22034/ijsom.2023.109243.2271</p> </div> </div> </div> </div> </div> </div>   <section class="alternate padding-xxs"> </section>   <div class="container"> <footer id="footer"> <div class="scrollup" id="scroll" href="#"><span></span></div> <div class="row"> <div class="col-md-2">  <h4 class="">Explore Journal</h4> <ul class="footer-links list-unstyled"> <li id="fli_home"><a href="./">Home</a></li> <li id="fli_about"><a href="./journal/about">About Journal</a></li> <li id="fli_Edb"><a href="./journal/editorial.board">Editorial Board</a></li> <li id="fli_submit"><a href="./author">Submit Manuscript</a></li> <li id="fli_contactus"><a href="./journal/contact.us">Contact Us</a></li> <li id="fli_glossary"><a href="./journal/glossary">Glossary</a></li> <li id="fli_order_hrdj"><a href="./journal/subscription.form">Hard Copy Subscription</a></li> <li id="fli_sitemap"><a href="./sitemap.xml?usr">Sitemap</a></li> </ul>  </div> <div class="col-md-3">  <h4 class="">Latest News</h4> <ul class="footer-posts list-unstyled"> <li> <a href="./news?newsCode=173">SD of ISC: Sustainable Development of Intelligent Supply Chains based on Trends and Future Directions: Application of Novel Solution Techniques</a> <small class="ltr">2023-03-05</small> </li> </ul>  </div> <div class="col-md-3">  <div><p><a title="Linkedin" href="http://www.linkedin.com/company/ijsom?trk=eml-cp_mktg-btn-welcome-20120607%2F"><img src="images/linkedin.jpg" alt="linkedin" /></a></p></div>  </div> <div class="col-md-4">  <h4 class="">Newsletter Subscription</h4> <p>Subscribe to the journal newsletter and receive the latest news and updates</p> <form class="validate" action="" method="post" data-success="Subscription saved successfully." data-toastr-position="bottom-right"> <input type="hidden" name="_token" value="81116dc33a3531bcdb798e518cedce8ce958627897e5654c"/> <div class="input-group"> <span class="input-group-addon"><i class="fa fa-envelope"></i></span> <input type="email" id="email" name="email" required="required" class="form-control required sbs_email" placeholder="Enter your Email" oninvalid="this.setCustomValidity('Enter a valid email address.')" oninput="this.setCustomValidity('')"> <span class="input-group-btn"> <button class="btn btn-primary mybtn" type="submit">Subscribe</button> </span> </div> </form>   <div class="margin-top-20"> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Facebook"> <i class="fa fa-facebook-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Twitter"> <i class="fa fa-twitter-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Linkedin"> <i class="fa fa-linkedin-square" aria-hidden="true"></i> </a> <a class="noborder" href="./ju.rss" class="social-icon social-icon-border social-rss pull-left block" data-toggle="tooltip" data-placement="top" title="Rss"><i class="fa fa-rss-square" aria-hidden="true"></i></a> </div> </div> </div> <div class="copyright" style="position: relative"> <ul class="nomargin list-inline mobile-block"> <li>© Journal Management System. <span id='sp_crt'>Powered by <a target='_blank' href='https://www.sinaweb.net/'>Sinaweb</a></span></li> </ul> </div> </footer> </div>  </div>   <a href="#" id="toTop_old"></a>  <div id="preloader"> <div class="inner"> <span class="loader"></span> </div> </div>  <script type="text/javascript">var plugin_path = './themes/base/front/assets/plugins/';</script> <script type="text/javascript" src="./themes/base/front/assets/js/scripts.js?v=0.02"></script>   <script type="text/javascript"> $('ul.nav li.dropdown').hover(function() { if (window.matchMedia('(max-width: 767px)').matches) return; 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Two Novel Generalized Information Measures for Fuzzy Sets