Group decision making based on acceptable consistency analysis of interval linguistic hesitant fuzzy preference relations

Abstract

To represent decision makers’ qualitative uncertainty and hesitation judgments, interval linguistic hesitant fuzzy variables (ILHFVs) are efficient tools, which can be regarded as an expansion of interval linguistic variables (ILVs). Taking the merits of ILHFVs and preference relations, this paper focuses on group decision making (GDM) with interval linguistic hesitant fuzzy preference relations (ILHFPRs). By considering the consistency of ILHFPRs, a new definition of acceptable consistency is presented. Using the acceptable consistency index, some models are built to measure whether a given ILHFPR is acceptable consistent. If the consistency is unacceptable, some models are constructed to derive acceptable consistent ILHFPRs by considering the total adjustment and the number of adjusting ILVs. In order to cope with incomplete ILHFPRs, some models for obtaining the values of unknown ILVs are proposed. For GDM with ILHFPRs, an index for measuring the consensus degree of ILHFPRs is proposed. When ILHFPRs do not meet the requirement of the consensus, some models for enhancing the consensus degree are proposed. According to the analysis of acceptable additive consistency and consensus of ILHFPRs, a new method for GDM with ILHFPRs is proposed. In order to show the merits of the proposed GDM method, an application example is used.