A new approach to decision making with fuzzy preference relation based on generalized consistency

Fuzzy preference relations are widely used in decision making problems for representing decision maker´s opinions on the alternatives. A new approach has been presented based on generalized consistency to rank all the alternatives in the decision making with fuzzy preference relation. Based on the concepts of multiplicative consistency and additive consistency, we propose the generalized consistency of fuzzy preference relation. We give the sufficient conditions that make generalized consistency become multiplicative consistency or additive consistency. Furthermore, we construct two optimal models to obtain the priority vector to rank the given alternatives in the decision making for the fuzzy preference relation based on the deviation matrix. Finally, a numerical example shows that the developed approach is feasible.