Abstract
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.
Highlights
Fuzzy information is an objective information type, which is represented by fuzzy set (FS) [1]
Proof: here we only prove the boundedness of group generalized Pythagorean fuzzy weighted geometric (GGPFWG) operator
The main conclusions are as follows: (1) If the Generalized parameter (GP) is not used to judge the accuracy of fuzzy information, or if only a single GP is used to judge the accuracy of fuzzy information, the decision making (DM) result calculated by Pythagorean fuzzy weighted average (PFWA) (PFWG) operator or GPFWA (GPFWG) operator is prone to errors
Summary
Fuzzy information is an objective information type, which is represented by fuzzy set (FS) [1]. J. Feng et al.: Group Generalized Pythagorean Fuzzy Aggregation Operators and Their Application in DM the accuracy of fuzzy information after consulting the patient in detail, and adjusts the fuzzy information, the diagnosis result will become more accurate. For complex application problems, it is impossible to judge the accuracy of fuzzy information comprehensively by a single GP, and the single GP may be wrong In this case, the group generalized parameters (GGPs) are needed. In this paper GGPFWA operator and GGPFWG operator are applied to solve DM problems, and their effectiveness and feasibility of the proposed aggregation operators are verified by three DM cases. VOLUME 8, 2020 the definitions and theorems of the proposed operators, and proves them; Section 5 presents the properties that the proposed operators should satisfy, and proves them; Section 6 applies the proposed operators to solve the problems of pattern recognition, medical diagnosis and MCDM.
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