Decision making with interval-valued intuitionistic fuzzy preference relations based on additive consistency analysis

This paper discusses the theory and application of interval-valued intuitionistic fuzzy preference relations (IVIFPRs). To do this, we first introduce an additive consistency concept for IVIFPRs that can address the issues in previous ones. Then, several additive consistency-based programming models for judging the consistency of IVIFPRs and for determining missing values are constructed. Furthermore, an approach for calculating the interval-valued intuitionistic fuzzy priority weight vector is offered. With respect to group decision making with IVIFPRs, a consensus index is offered, and an interactive algorithm for improving the consensus level is proposed that can ensure the additive consistency. After that, a consensus analysis-based programming model for determining the weights of decision makers is built. Furthermore, a consistency-and-consensus-based group decision-making method that can address inconsistent and incomplete IVIFPRs is developed. Finally, a practical decision-making problem about evaluating talents in universities is offered to show the feasibility and efficiency of the new method.