Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making

• Published in: International journal of intelligent systems Vol. 35; no. 1; pp. 150 - 183
• Main Authors: Wang, Lei, Li, Na
• Format: Journal Article
• Language: English
• Published: New York Hindawi Limited 01-01-2020
• Subjects: Agglomeration; Decision making; Fuzzy sets; Hierarchies; Intelligent systems; interaction operational laws; multiple attribute decision making; Operators (mathematics); PBM operator; PFIPBM operator; Pythagorean fuzzy set
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.22204

The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.