Interval-Valued Intuitionistic Fuzzy Power Bonferroni Aggregation Operators and Their Application to Group Decision Making

The power Bonferroni mean (PBM) operator can take the advantages of power operator and Bonferroni mean operator, which can overcome the influence of the unreasonable attribute values and can also consider the interaction between two attributes. However, it cannot be used to process the interval-valued intuitionistic fuzzy numbers (IVIFNs). It is importantly meaningful to extend the PBM operator to IVIFNs. We extend PBM operator to process IVIFNs and propose some new PBM operators for IVIFNs and apply them to solve the multi-attribute group decision-making (MAGDM) problems. Firstly, the definition, properties, score function, and operational rules of IVIFNs are introduced briefly. Then, the power Bonferroni mean (IVIFPBM) operator, the weighted PBM (IVIFWPBM) operator, the power geometric BM (IVIFPGBM) operator, and the weighted power geometric BM (IVIFWPGBM) operator for IVIFNs are proposed. Furthermore, some deserved properties of them are explored, and several special cases are analyzed. The decision-making methods are developed to deal with the MAGDM problems with the information of the IVIFNs based on the proposed operators, and by an illustrative example, the proposed methods are verified, and their advantages are explained by comparing with the other methods. The proposed methods can effectively solve the MAGDM problems with the IVIFNs, and they can consider the interaction between two attributes and overcome the influence of the unreasonable attribute values.