Two decision making models based on newly defined additively consistent intuitionistic preference relation

In this paper, we introduce the concept called fuzzy non-preferred relation where the elements are interpreted as the non-preferred intensity of one alternative over another one. We divide an intuitionistic preference relation into the fuzzy preference relation part and the fuzzy non-preferred relation part . Based on this division, we propose a new definition of additive consistency of intuitionistic preference relation based on the traditional one. Then, we construct an optimization model for deriving intuitionistic fuzzy weights which can be ranked easily in individual decision making environment. And we develop an optimization model for deriving the collective intuitionistic fuzzy weights to address group decision making problems. Finally, two numerical examples are provided to illustrate the developed approaches.