Abstract
ABSTRACTBy using type-2 fuzzy sets and hesitant fuzzy sets, type-2 hesitant fuzzy sets are defined and their mathematical structure and characteristics are given. The relations of the structures of type-2 hesitant fuzzy sets and hesitant fuzzy sets are further studied. Consequently, we prove that type-2 hesitant fuzzy sets are the generalization of hesitant fuzzy sets. Type-2 hesitant fuzzy sets may deal with the problem that hesitant fuzzy sets can't have repeated memberships. Otherwise, a part of the special type-2 hesitant fuzzy sets can be changed into discrete type-2 fuzzy sets, but their operations have many differences. On dealing with the fact problems, type-2 hesitant fuzzy sets are the better methods to solve the problems and can be easy to get better results.
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