Group decision making with incomplete interval-valued linguistic intuitionistic fuzzy preference relations

Abstract

With the increasing complexity and indeterminacy intensity of the decision making environment, there is a growing lack of widespread utility of traditional preference representations. As a practical yet valid preference expression, interval-valued linguistic intuitionistic fuzzy preference relations (IVLIFPRs) can efficiently represent the pairwise cognitions qualitatively and provide the inclusive support. This study aims at forming a novel group decision making (GDM) method based on the consistency and consensus preference analysis for IVLIFPRs. First, the new concepts of additive consistency and acceptably additive consistency for IVLIFPRs are defined. Based on these definitions, two optimization models are constructed to obtain the incomplete information and acceptably additive consistent IVLIFPRs, respectively. Then, inspired by the Markov model, the derivation approach of DMs' weights is designed. Afterward, the consensus improving process is constructed under the premise of acceptable consistency and smallest information distortion. Accordingly, the normalized priority weights of alternatives are further determined. Thus, a mechanism for the GDM method with incomplete and unacceptably consistent IVLIFPRs is developed. Finally, an application and comparison analysis show that the proposed method comprehensively considers the key steps in the GDM process, so that the logical rationality and technical superiority are well guaranteed.