Group decision making based on multiplicative consistency and consensus of fuzzy linguistic preference relations

Abstract

Fuzzy linguistic preference relations (FLPRs) are an efficient way to express qualitative judgments of decision makers (DMs). This paper proposes a new group decision making (GDM) method based on the multiplicative consistency and consensus of FLPRs. First, we propose the concepts of consistency index and acceptable multiplicative consistent FLPRs. Then, we propose a method to improve the consistency of a FLPR, by which an acceptable multiplicative consistent FLPR is derived. Subsequently, we propose the consensus index for measuring the agreement among DMs. With respect to some FLPRs have an unacceptable multiplicative consistency and an unacceptable consensus, we propose an integer programming model to make both their consistency and consensus better to yield improved FLPRs with acceptable multiplicative consistency and consensus. Furthermore, the DMs’ comprehensive weight vector is determined. Then, we propose a new GDM algorithm following the multiplicative consistency and consensus of FLPRs. Finally, the feasibility and the applicability of the proposed GDM method are illustrated via an application example and some comparative analyses with the existing GDM methods.