Dual hesitant fuzzy interaction operators and their application to group decision making

Considering that there may exist some interactions between membership function and non-membership function of different dual hesitant fuzzy sets (DHFSs), in this paper we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of dual hesitant fuzzy aggregation operators are developed, including dual hesitant fuzzy weighted interaction averaging operator, dual hesitant fuzzy weighted interaction geometric operator, dual hesitant fuzzy ordered weighted interaction averaging operator, dual hesitant fuzzy ordered weighted interaction geometric operator, dual hesitant fuzzy hybrid interaction averaging operator, and dual hesitant fuzzy hybrid interaction geometric operator. The properties of these aggregation operators are investigated. The key advantage of these operators is that the interactions between non-membership function and membership function of different DHFSs are considered, and much more information provided by decision makers (DMs) has been taken into account. Additionally, approaches to multiple attributes decision-making are given based on the aggregation operators under hesitant fuzzy environment and an example is given to illustrate the application of DHFSs in group fore-casting.