Foundational theories of hesitant fuzzy sets and families of hesitant fuzzy sets
This work addresses a foundational gap in hesitant fuzzy set theory, which is incremental but necessary for theoretical development in uncertainty modeling.
The study tackled the problem of defining inclusion relationships for hesitant fuzzy sets, which are important for applications involving uncertainty, by proposing multiple types of such relationships and foundational propositions for these sets and their families.
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.