Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System
The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measur...
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MDPI AG
2020-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/2/195 |
| _version_ | 1798040362553442304 |
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| author | Haiyi Mao Rui Cai |
| author_facet | Haiyi Mao Rui Cai |
| author_sort | Haiyi Mao |
| collection | DOAJ |
| description | The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example. |
| first_indexed | 2024-04-11T22:06:35Z |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:06:35Z |
| publishDate | 2020-02-01 |
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| series | Entropy |
| spelling | doaj.art-d91ee900bf9d4f7cbfc2bc82a69b378d2022-12-22T04:00:42ZengMDPI AGEntropy1099-43002020-02-0122219510.3390/e22020195e22020195Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection SystemHaiyi Mao0Rui Cai1School of Computer and Information Science, Southwest University, No. 2 Tiansheng Road, BeiBei District, Chongqing 400715, ChinaBusiness College, Southwest University, No.160 Xueyuan Road, Rongchang District, Chongqing 402460, ChinaThe Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.https://www.mdpi.com/1099-4300/22/2/195pythagorean fuzzy numbernegationuncertainty measuretopsisrelative closeness indexservice supplier selection system |
| spellingShingle | Haiyi Mao Rui Cai Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System Entropy pythagorean fuzzy number negation uncertainty measure topsis relative closeness index service supplier selection system |
| title | Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System |
| title_full | Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System |
| title_fullStr | Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System |
| title_full_unstemmed | Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System |
| title_short | Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System |
| title_sort | negation of pythagorean fuzzy number based on a new uncertainty measure applied in a service supplier selection system |
| topic | pythagorean fuzzy number negation uncertainty measure topsis relative closeness index service supplier selection system |
| url | https://www.mdpi.com/1099-4300/22/2/195 |
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