Ranking objects from group decision making with interval-valued hesitant fuzzy preference relations in view of additive consistency and consensus

Abstract This paper focuses on preference relations with interval-valued hesitant fuzzy variables, namely, interval-valued hesitant fuzzy preference relations (IVHFPRs). This type of preference relations permits the decision makers to apply several intervals in [0, 1] to denote their uncertain hesitancy preferences, and the numbers of intervals in different interval-valued hesitant fuzzy variables may be different. This endows the decision makers with more flexibility to express their preferences for compared objects. To calculate the priority weight vector from IVHFPRs logically, this paper defines an additive consistency concept for IVHFPRs. Then, 0–1 mixed programming models are constructed to judge the additive consistency of IVHFPRs, and a method for deriving additively consistent IVHFPRs is introduced. Using the additive consistency based probabilistic distribution, two methods for calculating the priority weight vector from additively consistent IVHFPRs are proposed. In virtue of the second method, we further discuss group decision making with IVHFPRs. To do this, a group consensus index is defined, and an approach to increase the consensus level is offered. After that, a group decision-making method with incomplete and inconsistent IVHFPRs is presented. Finally, two practical examples are selected to show the application of the new method, and comparison analysis is also made.

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