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.
Highlights
Decision-making is a common and significant activity in daily life
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
We extend the GWBM and generalized weighted Bonferroni geometric mean (GWBGM) operators, as well as develop the dual generalized weighted BM (DGWBM) and dual generalized weighted Bonferroni geometric mean (DGWBGM) operators, because the two operators can only consider the interrelationship between any two intuitionistic fuzzy number (IFN)
Summary
Decision-making is a common and significant activity in daily life. In the past decades, decision-making problems in real life have become increasingly complicated because of the increasing complexity in economic and social management. Liu and Teng [6] introduced the normal intuitionistic fuzzy numbers and several new normal intuitionistic fuzzy aggregation operators and applied them to multiattribute group decision-making (MAGDM). Liu [11] used the Hamacher operations as basis to develop several new aggregation operators to fuse the interval-valued intuitionistic fuzzy information. Peng and Yang [28] developed several Choquet integral-based operators for the Pythagorean fuzzy information Several aggregation operators, such as the BM [29] and the Heronian mean (HM) [30], can capture the interrelationship between arguments. The main objective of this study is to investigate GBM in PFSs. This research aims to develop several new GBM aggregation operators for PFNs and a new approach to MAGDM with Pythagorean fuzzy information.
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