The recently proposed partitioned Bonferroni mean (PBM) can effectively deal with situations in which attributes are partitioned into several parts, and attributes in the same part are dependent, whereas the attributes in different parts are independent. The power average (PA) operator has the capacity of reducing the negative effects of decision makers’ unreasonable assessments on the decision result. To take advantages of PBM and PA, we propose a family of Pythagorean fuzzy aggregation operators based on the interaction operational laws of Pythagorean fuzzy numbers (PFNs), such as the Pythagorean fuzzy interaction power PBM (PFIPPBM), the Pythagorean fuzzy interaction power partitioned geometric Bonferroni mean (PFIPPGBM), and the weighted forms of PFIPPBM and PFIPPGBM. The proposed operators can not only handle the situations where attributes are partitioned into several parts and attributes in the same part are interrelated, but also reduce the bad influence of unreasonable assessments on the decision result, and simultaneously consider the interactions between membership and non-membership degrees. Based on the proposed operators, a novel approach to multiple attribute group decision making (MAGDM) is proposed and a numerical instance as well as comparative analysis is conducted to demonstrate the validity and superiorities of the proposed approach.
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