On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights
In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise informati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/8/1081 |
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| author | Ewa Roszkowska Bartłomiej Jefmański Marta Kusterka-Jefmańska |
| author_facet | Ewa Roszkowska Bartłomiej Jefmański Marta Kusterka-Jefmańska |
| author_sort | Ewa Roszkowska |
| collection | DOAJ |
| description | In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig’s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented. |
| first_indexed | 2024-03-09T09:57:52Z |
| format | Article |
| id | doaj.art-ef64223ad0ea4c37a4ecea9d7cb04699 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T09:57:52Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-ef64223ad0ea4c37a4ecea9d7cb046992023-12-01T23:40:11ZengMDPI AGEntropy1099-43002022-08-01248108110.3390/e24081081On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy WeightsEwa Roszkowska0Bartłomiej Jefmański1Marta Kusterka-Jefmańska2Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, PolandDepartment of Econometrics and Computer Science, Wroclaw University of Economics and Business, 53-345 Wrocław, PolandDepartment of Quality and Environmental Management, Wroclaw University of Economics and Business, 53-345 Wrocław, PolandIn this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig’s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.https://www.mdpi.com/1099-4300/24/8/1081fuzzy multi-criteria decision makingfuzzy synthetic measureintuitionistic fuzzy setsentropy weightsideal-pointanti-ideal point |
| spellingShingle | Ewa Roszkowska Bartłomiej Jefmański Marta Kusterka-Jefmańska On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights Entropy fuzzy multi-criteria decision making fuzzy synthetic measure intuitionistic fuzzy sets entropy weights ideal-point anti-ideal point |
| title | On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights |
| title_full | On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights |
| title_fullStr | On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights |
| title_full_unstemmed | On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights |
| title_short | On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights |
| title_sort | on some extension of intuitionistic fuzzy synthetic measures for two reference points and entropy weights |
| topic | fuzzy multi-criteria decision making fuzzy synthetic measure intuitionistic fuzzy sets entropy weights ideal-point anti-ideal point |
| url | https://www.mdpi.com/1099-4300/24/8/1081 |
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