The Hamacher Aggregation Operators and their Application to Decision Making with Hesitant Pythagorean Fuzzy Sets

As a generalization of intuitionistic fuzzy sets(IFSs), Pythagorean fuzzy sets(IPFSs) can deal with uncertain information more flexibly for its relaxing condition that the square sum of the membership and non-membership is less than 1. While in real world, the uncertainty and fuzziness universally exist, hesitant fuzzy sets(HFSs) is more efficient in expressing the hesitant situation for assigning a set of memberships and non-memberships instead of one. This article deals with the group decision-making problem based on Hesitant Pythagorean fuzzy sets(HPFSs). Firstly, with Hamacher aggregation operations, the Hamacher aggregation hesitant Pythagorean weighted averaging operator (HHPWA) is constructed. Then, we aggregate the information with the collective ones. Finally, an illustrative numerical example is presented to test the effectiveness of the proposed approach.