Iterative Algorithms to Manage the Consistency and Consensus for Group Decision-Making With Hesitant Multiplicative Preference Relations

In this article, we study how to manage the consistency and consensus in group decision-making (GDM) with hesitant multiplicative preference relations (HMPRs). First, an approach to develop the priority weight vector of an HMPR is presented. Then, the consistency index of an HMPR is defined for its consistency checking. Subsequently, we define an acceptable consistent HMPR and propose an iterative procedure to improve the consistency of an unacceptable consistent HMPR. As to the GDM with HMPRs, distance measures and proximity degrees are defined to derive the weights of the decision makers (DMs). Moreover, a consensus index is proposed for measuring the agreement degree of different DMs' judgments, and an iterative approach is offered to implement the consensus reaching process. In the sequel, an algorithm to GDM with HMPRs is put forward. Two numerical examples are covered to highlight the merits of the proposed algorithms.