Consistency-Based Algorithms for Decision-Making With Interval Fuzzy Preference Relations

This paper reviews and analyzes several consistency concepts for interval fuzzy preference relations (IFPRs). On the basis of the comparisons, one can find that Krejs additive and multiplicative consistency concepts are more reasonable and flexible. Considering the issues that previous methods cannot fully address regarding incomplete and inconsistent IFPRs, this paper studies incomplete and inconsistent IFPRs using custom programming models based on Krejs concepts. Meanwhile, programming models for judging the additive and multiplicative consistency of IFPRs are constructed, respectively. Considering the consensus of IFPRs in group decision-making, a consensus index is defined, and programming models for improving the consensus levels of individual IFPRs are built. On the basis of the consistency and consensus analysis, two consistency-based algorithms for group decision-making with inconsistent and incomplete IFPRs are offered. One method is based on Krejs additive consistency concept, and the other uses Krejs multiplicative consistency concept. Meanwhile, associated examples are provided to show the application of the new methods.