A consensus building model in group decision making with non-reciprocal fuzzy preference relations

Abstract

Group decision making (GDM) is a wisdom extracting process where a group of decision makers (DMs) could reach a consensus on the optimal solution to the choice problem with a finite set of alternatives. This paper reports a consensus model in GDM, where the opinions of experts are expressed as fuzzy preference relations (FPRs) without additively reciprocal property to cope with the existing uncertainty. The concept of non-reciprocal fuzzy preference relations (NrFPRs) is proposed to capture the considered situation. A novel additive consistency index is constructed to quantify the inconsistency degree of NrFPRs using the relationship of two column/row vectors. An optimization model is constructed, where a new fitness function is proposed by considering the consistency degrees of NrFPRs and the consensus level of a group of experts. A novel concept of acceptable consensus standard is proposed to characterize the acceptance of the consensus process. The particle swarm optimization (PSO) algorithm is utilized to solve the constructed optimization problem. As compared to the existing models, numerical results show that the proposed model can be used to effectively reach an optimal solution to a GDM problem with NrFPRs.