Approaches to group decision making with linguistic preference relations based on multiplicative consistency

A key step in group decision making (GDM) with linguistic preference relations (LPRs) is to derive the priority weight vector of the alternatives. However, the lack of consistency in GDM can lead to inconsistent conclusions. In this paper, two new GDM methods are developed to improve the multiplicative consistency of LPRs until they are acceptable, and the priority weight vector of the alternatives is derived from adjusted LPRs. First, the new concepts of order consistency and multiplicative consistency for LPRs are introduced. Then, a consistency index is defined to measure whether a LPR is of acceptable multiplicative consistency. Two linear optimization models are established to generate the normalized crisp weight vector for both individual and group LPRs with the principle of minimizing the deviation values. In addition, two GDM methods are investigated to improve LPRs with unacceptable multiplicative consistency until the adjusted LPRs are acceptable multiplicative consistent, and they can help the decision makers (DMs) to obtain the reasonable and reliable decision making results. Finally, several numerical examples are provided, and comparative analyses with existing approaches are performed to demonstrate that the proposed methods are both valid and practical to deal with GDM problems.