An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was recently introduced to efficiently deal with situations in which the membership and non-membership are represented as linguistic terms. In this paper, we study the issues of additive consistency and the derivation of the intuitionistic fuzzy weight vector of an IFLPR. First, the new concepts of order consistency, additive consistency and weak transitivity for IFLPRs are introduced, and followed by a discussion of the characterisation about additive consistent IFLPRs. Then, a parameterised transformation approach is investigated to convert the normalised intuitionistic fuzzy weight vector into additive consistent IFLPRs. After that, a linear optimisation model is established to derive the normalised intuitionistic fuzzy weights for IFLPRs, and a consistency index is defined to measure the deviation degree between an IFLPR and its additive consistent IFLPR. Furthermore, we develop an automatic iterative decision-making method to improve the IFLPRs with unacceptable additive consistency until the adjusted IFLPRs are acceptable additive consistent, and it helps the decision-maker to obtain the reasonable and reliable decision-making results. Finally, an illustrative example is provided to demonstrate the validity and applicability of the proposed method.