Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making

Pythagorean Fuzzy Interaction Muirhead Means with Their Application to Multi-Attribute Group Decision-Making

“…To show the validity and superiorities of the proposed operators, we conduct a comparative analysis. We solve the same problem by some existing MAGDM approaches including the SPFWA and the SPFWG operators in [22], the Pythagorean fuzzy ordered weighted averaging weighted averaging distance (PFOWAWAD) operator in [22], the Pythagorean fuzzy point (PFP) operator and generalized Pythagorean fuzzy point ordered weighted averaging (GPFPOWA) in [23], the Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA) operator in [24], the Pythagorean fuzzy Einstein ordered weighted geometric (PFEOWG) operator in [25,26], the Pythagorean fuzzy weighted Bonferroni mean (PFWBM) operator in [30], the Pythagorean fuzzy weighted geometric Bonferroni mean (PFWGBM) operator in [31], the generalized Pythagorean fuzzy weighted Bonferroni mean (GPFWBM) operator and generalized Pythagorean fuzzy Bonferroni geometric mean (GPFBGM) operator in [32], the dual generalized Pythagorean fuzzy weighted Bonferroni mean (DGPFWBM) operator and dual generalized Pythagorean fuzzy weighted Bonferroni geometric mean (DGPFWBGM) operator in [32], the Pythagorean fuzzy weighted Maclaurin symmetric mean (PFWMSM) operator in [33], the generalized Pythagorean fuzzy weighted Maclaurin symmetric mean (GPFWMSM) operator in [34], the Pythagorean fuzzy interaction ordered weighted averaging (PFIOWA) operator and the Pythagorean fuzzy interaction ordered weighted geometric (PFIOWG) operator in [38], the Pythagorean fuzzy weighted Muirhead mean (PFWMM) operator, and Pythagorean fuzzy weighted dual Muirhead mean (PFWDMM) operator [39]. Details can be found in Table 2.…”

“…The approaches in [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] are based on a simple weighted averaging operator. The weaknesses of these approaches are (1) they assume that all the input arguments are independent, which is somewhat inconsistent with reality; (2) they cannot consider the interrelationship among input arguments; (3) they cannot capture the interrelationship between membership degree and non-membership degrees.…”

“…In other words, the proposed method can effectively handle situations in which a membership degree or a non-membership degree is zero. Thus, the proposed method is more powerful and flexible than the methods in [21][22][23][24][25][26]. the main drawback of these operators is that they do not consider the relationship between membership degree and non-membership degree.…”

“…Aggregation operators are a central topic in MAGDM, as they can ingrate individual input data into collective ones, and rank the alternatives based on the collective value. In the past years, quite a few Pythagorean fuzzy operators have been proposed and been applied to MAGDM successfully [20][21][22][23][24][25][26]. However, the main shortcomings of these operators are:…”

Interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator and their application to group decision making

“…Like intuitionistic fuzzy aggregation operators, Pythagorean fuzzy aggregation operators are also become an interesting and important area for research, after the advent of Pythagorean fuzzy set theory. Several researchers in [19][20][21][22][23][24][25][26][27][28] introduced many aggregation operators for decision using Pythagorean fuzzy information.…”