A novel method to derive the intuitionistic fuzzy priority vectors from intuitionistic fuzzy preference relations

Deriving the priority vectors of the alternatives by preference relations is a vital research topic for decision making with preference information. In this paper, a novel method is provided to derive the intuitionistic fuzzy priority vectors (IFPVs) from intuitionistic fuzzy preference relations (IFPRs). Concretely, the multiplicative consistencies of IFPRs are characterized by the IFPVs and the group of constrained linear equations, respectively. Then, it is pointed out that there always exist $$2n-1$$ constrained preference values based on which an acceptably multiplicative consistency is proposed, and a method to check and repair the acceptably multiplicative consistency of a complete or incomplete IFPR by reducing the distance between the optimal IFPVs and the local ones is provided. Some examples are given to show how the models work, and comparisons with the existing methods are also offered to demonstrate the advantages of the proposed method.