Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned Bonferroni mean operators.

The partitioned Bonferroni mean (PBM) operator and the partitioned geometric Bonferroni mean (PGBM) operator assume that all attributes are partitioned into several parts, where the members in the same part are interrelated, while the members in different parts are not interrelated. They can be used to process multiple attribute group decision making (MAGDM) problems in which attributes are partitioned into serval parts. In this paper, we extend the PBM operator and the PGBM operator based on the interaction operational laws of intuitionistic fuzzy sets (IFSs) to propose the interaction PBM (IFIPBM) operator for intuitionistic fuzzy numbers (IFNs), the weighted interaction PBM (IFWIPBM) operator for IFNs, the interaction PGBM (IFIPGBM) operator for IFNs and the weighted interaction PGBM (IFWIPGBM) operator for IFNs. We also analyze some properties and some special cases of these proposed operators (including the IFIPBM operator, the IFWIPBM operator, the IFIPGBM and the IFWIPGBM operator). Based on the proposed IFWIPBM operator and the proposed IFWIPGBM operator, a novel MAGDM method for IFNs is proposed, and some examples are used to compare the experimental results of the proposed method with the ones of the existing methods. The experimental results show that the proposed method outperforms the existing methods for MAGDM with INFs.