Decision making with intuitionistic linguistic preference relations

To address the preferred and nonpreferred degrees of linguistic variables, this paper introduces intuitionistic linguistic preference relations (ILPRs) that apply intuitionistic linguistic variables (ILVs) to denote the decision makers' preferences. To judge the consistency of ILPRs, a consistent concept is introduced, and a consistency index is defined. When ILPRs are unacceptably inconsistent, a method to improve the consistency is introduced. Then, an approach to rank ILVs is introduced. In some situations where ILPRs might be incomplete, the consistency-based linear programming model is constructed to evaluate the missing values. Considering group decision making, a group consensus index is defined, and its several desirable properties are discussed. Meanwhile, an acceptability-based consistency and consensus approach is developed, and the associated example is offered to show the efficiency of the proposed procedure.