Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915248983769088 |
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| author | Lu, Shizhan Xu, Zeshui Fu, Zhu Cheng, Longsheng Yang, Tongbin |
| author_facet | Lu, Shizhan Xu, Zeshui Fu, Zhu Cheng, Longsheng Yang, Tongbin |
| contents | Hesitant fuzzy sets find extensive application in specific scenarios involving uncertainty and hesitation. In the context of set theory, the concept of inclusion relationship holds significant importance as a fundamental definition. Consequently, as a type of sets, hesitant fuzzy sets necessitate a clear and explicit definition of the inclusion relationship. Based on the discrete form of hesitant fuzzy membership degrees, this study proposes multiple types of inclusion relationships for hesitant fuzzy sets. Subsequently, this paper introduces foundational propositions related to hesitant fuzzy sets, as well as propositions concerning families of hesitant fuzzy sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04256 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets Lu, Shizhan Xu, Zeshui Fu, Zhu Cheng, Longsheng Yang, Tongbin Artificial Intelligence Information Theory Machine Learning Hesitant fuzzy sets find extensive application in specific scenarios involving uncertainty and hesitation. In the context of set theory, the concept of inclusion relationship holds significant importance as a fundamental definition. Consequently, as a type of sets, hesitant fuzzy sets necessitate a clear and explicit definition of the inclusion relationship. Based on the discrete form of hesitant fuzzy membership degrees, this study proposes multiple types of inclusion relationships for hesitant fuzzy sets. Subsequently, this paper introduces foundational propositions related to hesitant fuzzy sets, as well as propositions concerning families of hesitant fuzzy sets. |
| title | Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets |
| topic | Artificial Intelligence Information Theory Machine Learning |
| url | https://arxiv.org/abs/2311.04256 |