Hybrid aggregation operators based on Pythagorean hesitant fuzzy sets and their application to group decision making

Pythagorean hesitant fuzzy set (PHFS) is a powerful tool to deal with uncertainty and vagueness. Therefore, based on Pythagorean hesitant fuzzy information in this paper we develop hybrid aggregation operators for Pythagorean hesitant fuzzy information namely, Pythagorean hesitant fuzzy hybrid weighted averaging operator, Pythagorean hesitant fuzzy hybrid weighted geometric operator. These developed operators can weigh both the argument and their ordered positions. Additionally, some numerical examples are given to illustrate the developed operators. Moreover we develop a multi-attribute group decision making approach based on the proposed operators. Finally, we give a numerical example to show the effectiveness and flexibility of the proposed method.