Consistency and consensus of intuitionistic fuzzy preference relations in group decision making

Abstract

Intuitionistic fuzzy preference relations (IFPRs) have turned out to be a useful structure in expressing the experts’ uncertain judgments. In this chapter, we consider a group decision making problem where all the members of the group use the IFPRs to express their preferences over the candidate alternatives. Firstly, we describe such a group decision making problem mathematically in details. Then, different types of definitions for the consistency of an IFPR are reviewed, which can be divided into two sorts, i.e., the additive consistency and the multiplicative consistency. Once all the IFPRs are of acceptable consistency, we then introduce a consensus measure to depict the consensus degree of the experts. A consensus reaching procedure is given to help the experts modify their assessments and then obtain an agreement between the experts as to the choice of a proper decision. A numerical example is given to show the validation and computational process of the consensus reaching procedure.