Algorithm for improving additive consistency of linguistic preference relations with an integer optimization model

Abstract Linguistic preference relation (LPR) composed by linguistic terms can well express decision makers’ (DMs’) qualitative preference opinion by comparing alternatives with each other. The investigation of its consistency becomes an important issue to guarantee the rationality of the decision making solutions. Therefore, it is significant to investigate the consistency measure and the consistency improving approach for LPRs. In this paper we present a new method for group decision making (GDM) with LPRs. First, an additive consistency index is introduced on the basis of the information of the original LPR to check whether a LPR is acceptably additive consistency. For unacceptably additively consistent LPR, an integer optimization model is further developed to obtain the acceptably additively consistent LPR. Moreover, the optimization model can guarantee the integrity of the information of the LPR with acceptably additive consistency. Then, with respect to GDM with LPRs, an entropy weight method is proposed to determine the weights of DMs. Finally, the proposed methods are implemented in two numerical examples including a GDM problem. Meanwhile, the comparative analysis with existing methods are discussed in detail to demonstrate the validity of the proposed methods.