Pythagorean fuzzy power Muirhead mean operators with their application to multi-attribute decision making

The sum of membership and non-membership degrees of the Pythagorean fuzzy set is greater than one with their square sum less than or equal to one. Thus, as an extension of intuitionistic fuzzy set, the Pythagorean fuzzy set is a powerful tool to describe fuzziness and uncertainty. The aim of this study is to introduce some new operators for aggregating Pythagorean fuzzy information and apply them to multi-attribute decision making. Considering the advantages of the power average operator and Muirhead mean, we introduce the power Muirhead mean operator and investigate it under Pythagorean fuzzy environment. Thus, some new Pythagorean fuzzy aggregation operators, such as the Pythagorean fuzzy power Muirhead mean and the weighted Pythagorean fuzzy power Muirhead mean are developed. The prominent advantage of these proposed operators is that they consider the relationships between fused data and the interrelationships between all aggregated values, thereby obtaining more information in the process of multi-attribute decision making. Furthermore, we introduce a novel approach to multi-attribute decision-making problems based on the proposed operators. Finally, we provide a numerical example to illustrate the validity of the proposed approach.