Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making

• We research a series of new aggregation operators based on Hamacher t-norm and t-conorm for hesitant fuzzy information.
• Some Hamacher operational rules of hesitant fuzzy sets are developed.
• A wide range of new hesitant fuzzy aggregation operators is proposed.
• We investigate their desirable properties and discuss the relationships between them.
• The proposed aggregation operators have more flexible for multicriteria decision making under hesitant fuzzy information environment.

As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. We first introduce some new operational rules of hesitant fuzzy sets based on the Hamacher t-norm and t-conorm, in which a family of hesitant fuzzy Hamacher operators is proposed for aggregating hesitant fuzzy information. Some basic properties of these proposed operators are given, and the relationships between them are shown in detail. We further discuss the interrelations between the proposed aggregation operators and the existing hesitant fuzzy aggregation operators. Applying the proposed hesitant fuzzy operators, we develop a new technique for hesitant fuzzy multicriteria decision making problems. Finally, the effectiveness of the proposed technique is illustrated by mean of a practical example.