A novel additive consistency for intuitionistic fuzzy preference relations

Abstract

Intuitionistic fuzzy preference relations (IFPRs), as an effective tool for expressing pair-wise comparisons between alternatives, has a great advantage in group decision making (GDM). The manuscript first compares and analyzes the existing definitions of additive consistency for IFPRs and points out the shortcomings of the existing definitions of additive consistency for IFPRs. To fill these gaps, a new definition of additive consistency for IFPRs is proposed Meanwhile, a mathematical programming model is presented to check whether an IFPR is additively consistent or not. In addition, for an inconsistent IFPR, a mathematical programming model is put forward to improve the consistent level. Furthermore, based on the mathematical programming model, a new individual marking decision method with IFPR is proposed, and the merits of the proposed method is analyzed through a associated example.