Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets

Name: Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets
Keywords: FOS: Computer and information sciences, Computer Science - Machine Learning, Artificial Intelligence (cs.AI), Computer Science - Artificial Intelligence, Computer Science - Information Theory, Information Theory (cs.IT), Machine Learning (cs.LG)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2023Embargo end date: 01 Jan 2023Publisher:arXiv

Authors: Lu, Shizhan; Xu, Zeshui; Fu, Zhu; Cheng, Longsheng; Yang, Tongbin;

doi: 10.48550/arxiv.2311.04256

arXiv: http://arxiv.org/abs/2311.04256

Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets

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Abstract

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.

15 pages

Keywords

FOS: Computer and information sciences, Computer Science - Machine Learning, Artificial Intelligence (cs.AI), Computer Science - Artificial Intelligence, Computer Science - Information Theory, Information Theory (cs.IT), Machine Learning (cs.LG)

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