A consistency and consensus-based method for group decision making with hesitant fuzzy linguistic preference relations

Abstract

Hesitant fuzzy linguistic preference relations (HFLPRs) can well denote the decision makers (DMs)’ hesitant qualitative comparison judgments. Considering that consistency and consensus are two key issues in group decisionmaking (GDM), this paper discusses GDM with HFLPRs within the context of multiplicative consistency and consensus. First, a multiplicative consistency concept for linguistic preference relations (LPRs) is presented, and a method for obtaining the priority weight vectors of LPRs is offered. Then, a method of deriving the priority weight vector of a HFLPR is proposed. Furthermore, the consistency index of a HFLPR is defined, an acceptable multiplicative consistency definition for HFLPRs is offered. Subsequently, for a HFLPR which has unacceptable consistency, an algorithm to improve its consistency level is developed. With respect to GDM with HFLPRs, a method to calculate the DMs’ weights is provided. Then, individual HFLPRs are integrated into a collective HFLPR. After that, a consensus index is defined, and an algorithm to improve the consensus is proposed that can guarantee the multiplicative consistency of individual HFLPRs. Moreover, an automatic algorithm to GDM with HFLPRs is developed. Lastly, we apply the new methods to two practical problems to verify their operability and applicability.