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

Abstract

This paper proposes a new group decision making (GDM) method based on the consistency and the consensus analysis of dual multiplicative linguistic preference relations (DMLPRs). A new type of linguistic variables , called dual multiplicative linguistic variables (DMLVs), is presented, which is defined on the multiplicative linguistic scale. DMLVs are used to represent asymmetrical qualitative hesitancy judgments of decision makers (DMs). A maximum-consistency-based interactive algorithm to derive multiplicative linguistic intuitionistic preference relations (MLIPRs) is presented, by which the consistency concept for DMLPRs is obtained. Then, we define the concept of inconsistent DMLPRs and propose an optimal-model-based method for deriving consistent DMLPRs. Furthermore, incomplete DMLPRs also can be dealt with by the proposed maximum-consistency-based interactive algorithm. For GDM, the weights of DMs are determined by the cosine-based correlation coefficient between individual DMLPRs. Moreover, we propose a consensus measure to calculate the agreement degree of DMLPRs and build an optimal model to increase the consensus level of individual DMLPRs. Finally, a new GDM method (call Algorithm III ) is offered and an application example is used to illustrate the proposed GDM method. The proposed GDM method outperforms the former GDM methods for GDM in the environments of DMLPRs.