The new generalized averaging aggregation operators and their application on group decision making problem base on interval-valued Pythagorean fuzzy numbers

The objective of this paper is to present the concept of the Interval-valued Pythagorean fuzzy set (IVPFS). Interval-valued Pythagorean fuzzy set is one of the successful extensions of the interval-valued intuitionistic fuzzy set. Under this environment, in this paper we introduced the notion of some generalized aggregation operation such as generalized interval-valued Pythagorean fuzzy weighted averaging (GIVPFWA) operator, generalized interval-valued Pythagorean fuzzy ordered weighted averaging (GIVPFOWA) operator, generalized interval-valued Pythagorean fuzzy hybrid averaging (GIVPFHA) operator long with their desirable properties namely, idempotency, boundedness and monotonicity. The main advantage and merits of using the proposed operators is that these operators give a complete view of the problem to the decision makers. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in real world problems. Finally the proposed operators have been applied to decision making problems to show the validity and effectiveness of the new approach.