Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

Abstract

The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.

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.…”

“…Approaches based on GPFWBM and GPFWBGM operators are better than approaches in [32], as the former approaches can capture the interrelationship between any three approaches. Approaches in [33,34] can consider the interrelationship among multiple arguments; however, all the methods [30][31][32][33][34] fail to reflect the interrelationship among all input arguments. Additionally, these methods do not consider the interrelationship among membership degree and non-membership degree.…”

“…The approaches in [32] based on the DGPFWBM and GPFWBGM operators are much better than the methods in [30][31][32][33][34], as they can consider the interrelationship among all arguments. Additionally, they have vectors of the parameters, leading to a flexible and feasible aggregation process.…”

“…Liang et al [30,31] proposed some Pythagorean fuzzy Bonferroni mean and geometric Bonferroni mean operators, respectively. Zhang et al [32] investigated the generalized Bonferroni mean to aggregate Pythagorean fuzzy information and proposed a family of Pythagorean fuzzy generalized Bonferroni means. Wei and Lu [33], and Qin [34] proposed some Pythagorean fuzzy Maclaurin symmetric mean operators, respectively.…”

Models for Multiple Attribute Decision-Making with Dual Generalized Single-Valued Neutrosophic Bonferroni Mean Operators

“…Zhang et al [34] develop the dual generalized WBM (DGWBM) operator and dual generalized WGBM (DGWGBM) operator. Definition 4 [34].…”