Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making

The Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters, but it only can deal with crisp values. In recent years, many extended BM operators have been proposed to deal with fuzzy information. Dombi Bonferroni mean operators are special cases of general T-conorm and T-norm, which have the advantage of good flexibility with a general parameter. In this paper, we extend the BM operator based on the Dombi operations to propose the intuitionistic fuzzy Dombi Bonferroni mean (IFDBM) operator, the intuitionistic fuzzy weighted Dombi Bonferroni mean (IFWDBM) operator, the intuitionistic fuzzy Dombi geometric Bonferroni mean (IFDGBM) operator and the intuitionistic fuzzy weighted Dombi geometric Bonferroni mean (IFWDGBM) operator for dealing with the aggregation of intuitionistic fuzzy numbers (IFNs) and propose some multi-attribute group decision-making (MAGDM) methods. Firstly, we introduce the concept, the characteristics, the score function, the accuracy function and the operational rules of IFNs. Then, we propose the IFDBM operator, the IFWDBM operator, the IFDGBM operator and the IFWDGBM operator for aggregating IFNs. Then, we propose two MAGDM methods based on the proposed IFWDBM operator and the proposed IFWDGBM operator for dealing with MAGDM problems. Finally, we use an example to illustrate the MAGDM process of the proposed MAGDM methods. The proposed intuitionistic fuzzy Dombi Bonferroni mean operators are very useful to deal with MAGDM problems.