Group decision making based on acceptable multiplicative consistency of hesitant fuzzy preference relations

Abstract

This paper deals with group decision making (GDM) with hesitant fuzzy preference relations (HFPRs) based on the acceptable multiplicative consistency and the consensus analysis. We first offer a multiplicative consistency index for fuzzy preference relations (FPRs) and then use the Monte Carlo simulation method to derive the average multiplicative consistency value. After that, a model-based interactive algorithm is offered to test acceptable multiplicative consistency of HFPRs, by which the concept of acceptable multiplicative consistency for HFPRs is obtained. Meanwhile, a model-based interactive algorithm for deriving acceptable multiplicative consistent HFPRs from unacceptable multiplicative consistent ones is provided, where both the total adjustment and the number of adjusted variables are considered. As for incomplete HFPRs, a model-based interactive algorithm for getting the values of missing preferences is provided. Furthermore, the weights of the decision makers are determined by the offered model and an algorithm of model-based adjustment for the consensus level is provided. Finally, a procedure for GDM with acceptable multiplicative consistent HFPRs is given, and a case study about selecting the most suitable project management information systems (PMISs) is provided to show the application of the proposed GDM method and to compare the proposed GDM method with the previous GDM methods.