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. (C) 2018 Published by Elsevier Inc.