A novel additive consistency for intuitionistic fuzzy preference relations in group decision making

Deriving the priority vectors of the alternatives from preference relations is an interesting research topic for group decision making with preference information. This paper uses an example to show that the ranking or the optimal alternative could not always be derived from the existing additively consistent intuitionistic fuzzy preference relations. Thus, we provide novel additively consistent intuitionistic fuzzy preference relations and characterize them with Tanino’s normalized (T-normalized) intuitionistic fuzzy priority vectors. Then, we propose some methods to check and achieve the T-normalization, acceptably additive consistency and consensus of the intuitionistic fuzzy preference relations in group decision making using the local, individual and optimal collective intuitionistic fuzzy priority vectors, respectively. We also give some examples to show how the proposed models work and make comparisons with the existing methods to demonstrate the advantages of the proposed methods.