Consensus Reaching with Minimum Adjustment and Consistency Management in Group Decision Making with Intuitionistic Multiplicative Preference Relations

Intuitionistic multiplicative preference relation (IMPR) is an efficient tool for describing the paired comparisons between objectives in group decision making (GDM). Existing GDM methods with IMPRs overlook the hesitancy of IMPRs and lack a feedback mechanism of adjustment in the consensus reaching process (CRP). Thus, to ensure that the adjusted IMPRs can provide reliable information for decision making, the hesitancy measure for IMPRs is first incorporated into the process of enhancing consistency and consensus. A new consistency index for IMPRs is defined based on distance measure. Some goal programming models are constructed for enhancing consistency of IMPR. For a collection of IMPRs with unacceptable consistency and consensus, based on the optimization model and the identification rule and direction rule (IR-DR), an interactive iterative algorithm is designed for enhancing consistency and consensus, which can greatly save the completion time of consensus reaching and maintain primitive information to the maximum. Subsequently, a distance-based aggregation model is constructed to derive the group IMPR by considering different experts’ decision-making principles. Thereby, a new GDM method with IMPRs considering minimum adjustment is proposed. Moreover, the rationality and effectiveness of the proposed method are verified through a numerical example and some related simulation experiments. Meanwhile its merits are illustrated by comparison analyses.