Group Generalized Pythagorean Fuzzy Aggregation Operators and Their Application in Decision Making

Fuzzy information is generally represented by fuzzy set (FS). Pythagorean fuzzy set (PFS), as a new extension of FS, can represent fuzzy information more effectively. The accuracy of fuzzy information represented by PFS directly affects the result of information processing. Generalized parameter (GP), expressed by Pythagorean fuzzy number, can judge the accuracy of fuzzy information represented by PFS. However, for complex fuzzy application problems, a single GP cannot comprehensively judge the fuzzy information, and the GP may also be wrong. Therefore, the concept of group generalized parameters (GGPs) is proposed. The GGPs can comprehensively judge the accuracy of fuzzy information, and can avoid the influence caused by the error of a certain GP. In order to effectively aggregate the fuzzy information and the GGPs, some new group generalized Pythagorean fuzzy aggregation operators are proposed, including group generalized Pythagorean fuzzy weighted average (GGPFWA) operator and group generalized Pythagorean fuzzy weighted geometric (GGPFWG) operator. The definitions, theorems and properties of GGPFWA operator and GGPFWG operator are given and proved. In this paper, GGPFWA operator and GGPFWG operator are applied to solve decision making problems, and their effectiveness and feasibility have been verified by three cases of pattern recognition, medical diagnosis and multiple criteria decision making.