Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making
The consolidation of evaluations from various decision-makers within a group, concerning multiple attributes of limited schemes, seeks to unify or compromise collective preferences according to specific rules. The superior characteristics of Possibility Fuzzy Sets (PFS) in membership endow it with e...
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| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231452?viewType=HTML |
| _version_ | 1797635372943933440 |
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| author | Wei Lu Yuangang Li Yixiu Kong Liangli Yang |
| author_facet | Wei Lu Yuangang Li Yixiu Kong Liangli Yang |
| author_sort | Wei Lu |
| collection | DOAJ |
| description | The consolidation of evaluations from various decision-makers within a group, concerning multiple attributes of limited schemes, seeks to unify or compromise collective preferences according to specific rules. The superior characteristics of Possibility Fuzzy Sets (PFS) in membership endow it with enhanced capabilities in depicting ambiguous information. The Bonferroni operator proficiently mitigates the influences of interrelations between attributes in decision-making dilemmas. To address the Multi-Attribute Decision Making (MADM) conundrum wherein attribute values are associative Triangular Pythagorean Fuzzy Numbers (TPFNs), a novel methodology leveraging the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Mean (GTPFWBM) operator and the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Geometric Mean (GTPFWBGM) operator is advanced. Initiating with the foundational Triangular Pythagorean Fuzzy Set and the Generalized Bonferroni Mean (GBM) operator, both the GTPFWBM and GTPFWBGM operators are delineated. Subsequent exploration dives into the intrinsic properties of these pioneering operators, encompassing facets like reducibility, permutation invariance, idempotency, monotonicity and boundedness. Building upon this foundation, a MADM methodology predicated on the GTPFWBM and GTPFWBGM operators is conceptualized. The culmination of this research underscores the method's rationality and practicality, illustrated through a venture capital investment exemplar. |
| first_indexed | 2024-03-11T12:21:09Z |
| format | Article |
| id | doaj.art-ce8848545f3e4cd3bfd4c73c14f60e72 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T12:21:09Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ce8848545f3e4cd3bfd4c73c14f60e722023-11-07T01:14:17ZengAIMS PressAIMS Mathematics2473-69882023-10-01812283762839710.3934/math.20231452Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-makingWei Lu0Yuangang Li1Yixiu Kong 2Liangli Yang 31. Personnel Division, Shanghai University of Political Science and Law, Shanghai 201701, China2. Faculty of Business Information, Shanghai Business School, Shanghai, 200235, China3. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100872, China3. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100872, ChinaThe consolidation of evaluations from various decision-makers within a group, concerning multiple attributes of limited schemes, seeks to unify or compromise collective preferences according to specific rules. The superior characteristics of Possibility Fuzzy Sets (PFS) in membership endow it with enhanced capabilities in depicting ambiguous information. The Bonferroni operator proficiently mitigates the influences of interrelations between attributes in decision-making dilemmas. To address the Multi-Attribute Decision Making (MADM) conundrum wherein attribute values are associative Triangular Pythagorean Fuzzy Numbers (TPFNs), a novel methodology leveraging the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Mean (GTPFWBM) operator and the Generalized Triangular Pythagorean Fuzzy Weighted Bonferroni Geometric Mean (GTPFWBGM) operator is advanced. Initiating with the foundational Triangular Pythagorean Fuzzy Set and the Generalized Bonferroni Mean (GBM) operator, both the GTPFWBM and GTPFWBGM operators are delineated. Subsequent exploration dives into the intrinsic properties of these pioneering operators, encompassing facets like reducibility, permutation invariance, idempotency, monotonicity and boundedness. Building upon this foundation, a MADM methodology predicated on the GTPFWBM and GTPFWBGM operators is conceptualized. The culmination of this research underscores the method's rationality and practicality, illustrated through a venture capital investment exemplar.https://www.aimspress.com/article/doi/10.3934/math.20231452?viewType=HTMLtriangular pythagorean fuzzy setgeneralized triangular pythagorean fuzzy weighted bonferroni mean operatorgeneralized triangular pythagorean fuzzy weighted bonferroni geometric mean operatormulti-attribute decision making |
| spellingShingle | Wei Lu Yuangang Li Yixiu Kong Liangli Yang Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making AIMS Mathematics triangular pythagorean fuzzy set generalized triangular pythagorean fuzzy weighted bonferroni mean operator generalized triangular pythagorean fuzzy weighted bonferroni geometric mean operator multi-attribute decision making |
| title | Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making |
| title_full | Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making |
| title_fullStr | Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making |
| title_full_unstemmed | Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making |
| title_short | Generalized triangular Pythagorean fuzzy weighted Bonferroni operators and their application in multi-attribute decision-making |
| title_sort | generalized triangular pythagorean fuzzy weighted bonferroni operators and their application in multi attribute decision making |
| topic | triangular pythagorean fuzzy set generalized triangular pythagorean fuzzy weighted bonferroni mean operator generalized triangular pythagorean fuzzy weighted bonferroni geometric mean operator multi-attribute decision making |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231452?viewType=HTML |
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