Pythagorean fuzzy linguistic Muirhead mean operators and their applications to multiattribute decision-making

Pythagorean fuzzy sets, as an extension of intuitionistic fuzzy sets to deal with uncertainty, have attracted much attention since their introduction, in both theory and application aspects. In this paper, we investigate multiple attribute decision-making (MADM) problems with Pythagorean linguistic information based on some new aggregation operators. To begin with, we present some new Pythagorean fuzzy linguistic Muirhead mean (PFLMM) operators to deal with MADM problems with Pythagorean fuzzy linguistic information, including the PFLMM operator, the Pythagorean fuzzy linguistic-weighted Muirhead mean operator, the Pythagorean fuzzy linguistic dual Muirhead mean operator and the Pythagorean fuzzy linguistic dual-weighted Muirhead mean operator. The main advantages of these aggregation operators are that they can capture the interrelationships of multiple attributes among any number of attributes by a parameter vector and make the information aggregation process more flexible by the parameter vector . In addition, some of the properties of these new aggregation operators are proved and some special cases are discussed where the parameter vector takes some different values. Moreover, we present two new methods to solve MADM problems with Pythagorean fuzzy linguistic information. Finally, an illustrative example is provided to show the feasibility and validity of the new methods, to investigate the influences of parameter vector on decision-making results, and also to analyze the advantages of the proposed methods by comparing them with the other existing methods.