Some Methods Considering Multiplicative Consistency and Consensus in Group Decision Making with Interval-Valued Intuitionistic Fuzzy Preference Relations

In decision making with interval-valued intuitionistic fuzzy preference relations (IVIFPRs), the consistency and its improvement are key issues. The aim of this paper is to investigate a new multiplicative consistency of IVIFPRs based on interval arithmetic, and propose goal programming approach to improve consistency and consensus. Based on analysis of the drawbacks of the existing consistency definitions of IVIFPR, new definition for multiplicative consistent IVIFPR is introduced. Based on the proposed multiplicative consistency and analysis of the relationship between interval-valued intuitionistic fuzzy weights and multiplicative consistent IVIFPR, goal programming-based model is developed for deriving interval-valued intuitionistic fuzzy weights from IVIFPR. To measure the multiplicative consistency degree of IVIFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IVIFPR with unacceptable consistency, a mathematical programming approach is proposed to improve its consistency. By considering the experts’ subjective and consensus weights, the experts’ comprehensive weights are determined. Some numerical examples illustrate the proposed models.