Towards achieving consistent opinion fusion in group decision making with complete distributed preference relations

Belief distribution (BD) is a scheme of representing qualitative information with subjective uncertainty and imprecision. Distributed preference relation (DPR) extends BDs to the form of pairwise comparison by expressing the preferred, non-preferred, indifferent, and uncertain degrees of one decision alternative over another. However, previous studies on DPR only require comparison of adjacent alternatives, and consensus reaching is not considered fully in the decision making process. To solve this problem, a complete DPR model is presented in this paper to support group decision making (GDM). First, a consistency index is defined to measure the consistency level of the complete DPR representing experts’ judgments. Second, an automatic adjustment algorithm is proposed to improve the consistency of DPRs with unacceptable consistency to an acceptable level. Third, the evidential reasoning (ER) algorithm is utilized to aggregate all the DPRs together, and an optimization model is further constructed to generate experts’ weights, which maximizes the degree of consensus among experts. A GDM example is provided to illustrate the applicability and validity of the proposed DPR model, and comparative analysis demonstrates the potential of the proposed method in supporting real-world GDM problems.