{"title":"New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS","authors":"Xinxing Wu, Qian Liu, Lantian Liu, Miin-Shen Yang, Xu Zhang","doi":"10.1007/s40747-024-01761-0","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we first give an example to show that Theorem 1 in Hung and Yang (Inf Sci 178(6):1641–1650, 2008) does not hold, implying that the <i>J</i>-divergence introduced by Hung and Yang does not satisfy the axiomatic definition of intuitionistic fuzzy divergence measure. Inspired by this, a new Jensen–Shannon divergence measure for intuitionistic fuzzy sets (IFSs) is introduced and some basic properties for this new divergence measure are obtained. In particular, this divergence measure, and its induced similarity measure, and induced entropy measure satisfy the axiomatic definitions of divergence, similarity, and entropy for IFSs. Based on our proposed divergence measure, entropy measure, and entropy-weight method, a new TOPSIS method is introduced to deal with multi-attribute decision making (MADM) problems under the intuitionistic fuzzy framework. Finally, a practical example on the credit evaluation of potential strategic partners and a comparative analysis with other TOPSIS methods is developed to illustrate the efficiency of the proposed TOPSIS method.</p>","PeriodicalId":10524,"journal":{"name":"Complex & Intelligent Systems","volume":"342 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex & Intelligent Systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s40747-024-01761-0","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we first give an example to show that Theorem 1 in Hung and Yang (Inf Sci 178(6):1641–1650, 2008) does not hold, implying that the J-divergence introduced by Hung and Yang does not satisfy the axiomatic definition of intuitionistic fuzzy divergence measure. Inspired by this, a new Jensen–Shannon divergence measure for intuitionistic fuzzy sets (IFSs) is introduced and some basic properties for this new divergence measure are obtained. In particular, this divergence measure, and its induced similarity measure, and induced entropy measure satisfy the axiomatic definitions of divergence, similarity, and entropy for IFSs. Based on our proposed divergence measure, entropy measure, and entropy-weight method, a new TOPSIS method is introduced to deal with multi-attribute decision making (MADM) problems under the intuitionistic fuzzy framework. Finally, a practical example on the credit evaluation of potential strategic partners and a comparative analysis with other TOPSIS methods is developed to illustrate the efficiency of the proposed TOPSIS method.
期刊介绍:
Complex & Intelligent Systems aims to provide a forum for presenting and discussing novel approaches, tools and techniques meant for attaining a cross-fertilization between the broad fields of complex systems, computational simulation, and intelligent analytics and visualization. The transdisciplinary research that the journal focuses on will expand the boundaries of our understanding by investigating the principles and processes that underlie many of the most profound problems facing society today.