New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS
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,...
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| Format: | Article |
| Language: | English |
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Springer
2025-01-01
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| Series: | Complex & Intelligent Systems |
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| Online Access: | https://doi.org/10.1007/s40747-024-01761-0 |
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| author | Xinxing Wu Qian Liu Lantian Liu Miin-Shen Yang Xu Zhang |
| author_facet | Xinxing Wu Qian Liu Lantian Liu Miin-Shen Yang Xu Zhang |
| author_sort | Xinxing Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3248c45018294fe395b274d8cc9a1409 |
| institution | Kabale University |
| issn | 2199-4536 2198-6053 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Springer |
| record_format | Article |
| series | Complex & Intelligent Systems |
| spelling | doaj-art-3248c45018294fe395b274d8cc9a14092025-02-09T13:01:08ZengSpringerComplex & Intelligent Systems2199-45362198-60532025-01-0111211510.1007/s40747-024-01761-0New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSISXinxing Wu0Qian Liu1Lantian Liu2Miin-Shen Yang3Xu Zhang4School of Mathematics and Statistics, Guizhou University of Finance and EconomicsSchool of Sciences, Southwest Petroleum UniversitySchool of Sciences, Southwest Petroleum UniversityDepartment of Applied Mathematics, Chung Yuan Christian UniversityDepartment of Mathematics, Shandong UniversityAbstract 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.https://doi.org/10.1007/s40747-024-01761-0Fuzzy setsIntuitionistic fuzzy setsDivergence measuresSimilarity measuresEntropyMulti-attribute decision making (MADM) |
| spellingShingle | Xinxing Wu Qian Liu Lantian Liu Miin-Shen Yang Xu Zhang New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS Complex & Intelligent Systems Fuzzy sets Intuitionistic fuzzy sets Divergence measures Similarity measures Entropy Multi-attribute decision making (MADM) |
| title | New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS |
| title_full | New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS |
| title_fullStr | New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS |
| title_full_unstemmed | New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS |
| title_short | New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS |
| title_sort | new jensen shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy topsis |
| topic | Fuzzy sets Intuitionistic fuzzy sets Divergence measures Similarity measures Entropy Multi-attribute decision making (MADM) |
| url | https://doi.org/10.1007/s40747-024-01761-0 |
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