Pythagorean fuzzy average aggregation operators based on generalized and group-generalized parameter with application in MCDM problems

Abstract

The concept of intuitionistic fuzzy set (IFS) theory plays an important role in dealing with real‐life issues under uncertain and imprecise environment. But it has certain limitations and further extended by many researchers by taking different situations. One of the extensions of IFS theory is Pythagorean fuzzy set (PFS), in which the condition of IFS theory, ie, sum of membership degree and nonmembership degree is less than (or equal to) one is related to the square sum of its membership degree and nonmembership degree is less than (or equal to) one. In this study, the concept of the generalized parameter is incorporated into the PFS theory and presented some generalized Pythagorean fuzzy average aggregation operators. Then, the operators are extended to a group‐based generalized parameter by taking the opinions of multiple senior experts/observers. Based on the defined operators, a multi‐criteria decision‐making (MCDM) approach is provided and illustrated with a numerical example to show the proposed approach effectively. Finally, a comparison analysis is also considered to validate the proposed approach over the existing ones.

Group-based generalized q-rung orthopair average aggregation operators and their applications in multi-criteria decision making

“…Moreover, by comparing the superiorities and advantages of the developed approach with existing methods in the literature using the same example and ignoring the group generalized parameter matrix [Y] m×k . These methods including intuitionistic fuzzy weighted averaging (IFWA) operator presented by Xu [28] and Li [18], Pyhtagorean fuzzy weighted averaging (PFWA) operator presented by Yagger [32], Ma and Xu [22], symmetric Pythagorean fuzzy weighted averaging (SPFWA) operator presented by Ma and Xu [22], group generalized parameter Pythagorean fuzzy weighted averaging (GGPFWA) operator initiated by Joshi [17], q-ROFWA…”

“…The ranking result for the rest of MCDM methods remain same and the best optimal value is d 1 . But the methods proposed by Yager [32], Ma and Xu [22] and Joshi [17] have also some restriction and they cannot handle the assessment value satisfy…”

“…On the basis of PFS [31], Yager and Abassov [34] presented the notion of Pythagorean membership grade in PFS and they showed their application in decision making. Since the appearance of PF S many practitioners widely extended this remarkable concept in different directions such as, Yager [32] presented the idea of PF weighted average (PFWA) operator and PF weighted power average operator to aggregate the information, Peng and Yang [24] presented the detail study of division and subtraction operations in P F environment, Peng and Yuan [25] investigated the fundamental properties of point aggregation operators and their applications in MCDM, Garg presented the concepts of various aggregation operators in [8][9][10], Ma and Xu [22] initiated the notion of symmetric PF weighted averaging and geometric (SPFW A/G) operators, Hussain et al [16] presented rough PF ideals in semigroups, Joshi [17] presented the combine study of generalized parameter and PFWA operators to construct the concept of generalized PFWA (GPFWA), generalized PF ordered weighted average (GPFOWA), and generalized PF hybrid average (GPFHA) operators and Hussain et al [14] proposed the concept of PF soft rough set and their desirable properties with detail.…”

Confidence levelsq‐rung orthopair fuzzy aggregation operators and its applications to MCDM problems

“…Zhang et al extended the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduced the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Joshi presented some generalized Pythagorean fuzzy average aggregation operators by incorporating the concept of the generalized parameter to the Pythagorean fuzzy set theory.…”

Linguistic Pythagorean Einstein Operators and Their Application to Decision Making

“…Khan et al [45] developed an MADM approach based on a new ranking methodology with Pythagorean trapezoidal uncertain linguistic fuzzy information. More research results on the theories and techniques can be found in References [46][47][48][49][50][51].…”