Optimizing consistency and consensus improvement process for hesitant fuzzy linguistic preference relations and the application in group decision making

Abstract

Hesitant fuzzy linguistic preference relations (HFLPRs) are commonly used by decision makers when they are hesitant to express preferences. The use of HFLPRs in group decision-making (GDM) requires that the consistency of each HFLPR and consensus of the HFLPRs be acceptable. To ensure the reliability of using HFLPRs in GDM, a novel GDM model based on HFLPRs integrating the consistency and consensus improvement process is introduced. First, some novel consistency and consensus improvement methods by using an optimization technique are proposed for three actual cases: (1) the decision makers refuse to modify their opinions and the problem is without time pressure; (2) the decision makers are willing to modify their opinions and the problem is without time pressure; (3) the decision-making problem is under time pressure. For the former two cases, two iterative consistency and consensus improvement methods are introduced, and, for the last case, a method based on optimization models is introduced to modify the decision makers’ weights. A novel GDM model is given based on the proposed methods. Finally, an example is solved by using the proposed GDM model, and a comparison analysis is given.