Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making
Abstract As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-wor...
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Nature Portfolio
2025-02-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-84582-y |
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| author | Yanpo Yang Baoquan Ning Fengjuan Tian Guihui Lu |
| author_facet | Yanpo Yang Baoquan Ning Fengjuan Tian Guihui Lu |
| author_sort | Yanpo Yang |
| collection | DOAJ |
| description | Abstract As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive. |
| format | Article |
| id | doaj-art-ada346a988944d168f38e58968b08557 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-ada346a988944d168f38e58968b085572025-02-09T12:33:59ZengNature PortfolioScientific Reports2045-23222025-02-0115112610.1038/s41598-024-84582-ySome complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision makingYanpo Yang0Baoquan Ning1Fengjuan Tian2Guihui Lu3School of Mathematics and Statistics, Liupanshui Normal UniversitySchool of Mathematics and Statistics, Liupanshui Normal UniversitySchool of Mathematics and Statistics, Liupanshui Normal UniversitySchool of Mathematics and Statistics, Liupanshui Normal UniversityAbstract As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive.https://doi.org/10.1038/s41598-024-84582-yComplex probabilistic hesitant fuzzy setComplex probabilistic hesitant fuzzy elementAggregation operatorsMulti-attribute decision making |
| spellingShingle | Yanpo Yang Baoquan Ning Fengjuan Tian Guihui Lu Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making Scientific Reports Complex probabilistic hesitant fuzzy set Complex probabilistic hesitant fuzzy element Aggregation operators Multi-attribute decision making |
| title | Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making |
| title_full | Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making |
| title_fullStr | Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making |
| title_full_unstemmed | Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making |
| title_short | Some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi-attribute decision making |
| title_sort | some complex probabilistic hesitant fuzzy aggregation operators and their applications to multi attribute decision making |
| topic | Complex probabilistic hesitant fuzzy set Complex probabilistic hesitant fuzzy element Aggregation operators Multi-attribute decision making |
| url | https://doi.org/10.1038/s41598-024-84582-y |
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