Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations

Interval-valued hesitant fuzzy preference relations (IVHFPRs) are useful that allow decision makers to apply several intervals in [0, 1] to denote the uncertain hesitation preference. To derive the reasonable ranking order from group decision making with preference relations, two topics must be considered: consistency and consensus. This paper focuses on group decision making with IVHFPRs. First, a multiplicative consistency concept for IVHFPRs is defined. Then, programming models for judging the consistency of IVHFPRs are constructed. Meanwhile, an approach for deriving the interval fuzzy priority weight vector is introduced that adopts the consistency probability distribution as basis. Subsequently, this paper builds several multiplicative consistency-based programming models for estimating the missing values in incomplete IVHFPRs. A consensus index is introduced to measure the agreement degree between individual IVHFPRs, and a method for increasing the consensus level is presented. Finally, a multiplicative consistency-and-consensus-based group decision-making method with IVHFPRs is offered, and a practical decision-making problem is selected to show the application of the new method.