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. K E Y W O R D S interaction operational laws, multiple attribute decision making, PBM operator, PFIPBM operator, Pythagorean fuzzy set 1 | INTRODUCTIONMultiple attribute decision making (MADM) is an important research topic in decision science, which can be described as to select the best alternative from a set of feasible alternatives according to several attributes. Due to the increasing complexity and uncertainty in modern decision making activities, some influencing factors result in decision makers to often have difficulty in assigning crisp values or fuzzy values 1 described only by membership degree for each alternative with respect to each attribute. More recently, as an effective generalization of intuitionistic fuzzy sets (IFSs), 2 the concept of Pythagorean fuzzy sets (PFSs) was developed by Yager. 3,4 The PFSs expressed fuzzy information by using a membership degree and a nonmembership degree, and satisfied the condition that the square sum of its membership degree and nonmembership degree is less than or equal to 1. Obviously, PFSs are more powerful than fuzzy sets (FSs) and IFSs to describe some complex fuzzy information. [5][6][7][8] In recent years, as a novel evaluation, PFSs not only have been extensively studied in theory, but also have achieved a great number of achievements in applications, such as information measures, [9][10][11][12][13][14][15] basic operations, [16][17][18]11,13,[19][20][21][22][23][24][25][26][27][28] Especially the information aggregation operators, as an important role in MADM, have been proposed to aggregate Pythagorean fuzzy numbers (PFNs). For instance, Ma and Xu 29 developed the Pythagorean fuzzy weighted averaging (PFWA) operator and Pythagorean fuzzy weighted geometric (PFWG) operator, and also proposed symmetric Pythagorean fuzzy weighted averaging (SPFWA) operator and symmetric ...
