Group decision making based on relative projection between fuzzy preference relations

Abstract

Group decision making (GDM) has been widely focused on for coping with the complexity of a practical decision making problem. This paper proposes a relative projection-driven GDM model with fuzzy preference relations (FPRs). First, a novel additive consistency index of FPRs is constructed using the variance of relative projections between column/row vectors in two FPRs, which is called the relative projection variance consistency index (RPVCI). The thresholds of RPVCI for FPRs with acceptable additive consistency (AAC) are calculated using the simulation method. For improving consistency of FPRs, a convergent iteration algorithm is constructed by equipping subjective and objective adjustment parameters. Second, the group consensus level is captured using relative projections of individual FPRs on the collective one. An iteration model is reported to optimize the consensus degree by combining the weights of experts with a comprehensive adjustment coefficient that depends on both subjective and objective factors. Third, a novel GDM algorithm is proposed by integrating the two proposed iteration models. Comparisons with some existing models are offered by carrying out a case study to show the novelty and advantage of the proposed GDM model.