Pythagorean Fuzzy Bonferroni Mean with Weighted Interaction Operator and Its Application in Fusion of Online Multidimensional Ratings

Aiming at the aggregation problem of online multi-attribute interactive ratings, a decision-making method based on Pythagorean Fuzzy Bonferroni mean with weighted interaction (PFWIBM) operator is developed by mining the advantages of ratings driven decision-making and the quantitative advantages of Pythagorean fuzzy sets on linguistic ratings. First, the shortcomings of existing operators in criterion interactive representation are analyzed, and the improved Bonferroni mean with weighted interaction and its dual operator are defined, which are used to aggregate the membership information and non-membership information under the Pythagorean fuzzy environment, respectively, and then the PFWIBM operator is constructed. Second, a generation method of interaction coefficients embedded in the PFWIBM operator is designed by combining expert knowledge and user ratings to overcome the limitations of the method of relying on subjective setting parameter values. Third, based on the proposed operator and the transformation relationship between Pythagorean fuzzy sets and linguistic ratings, an online multi-dimensional rating aggregation decision-making approach for solving product raking problems is developed. Finally, the proposed method is applied to a passenger car ranking example to show the feasibility of the method, and through some comparative analysis, the advantages of the proposed operator are clarified, and the influence of operator parameters on the decision-making results is analyzed.