Consistency and consensus enhancing in group decision making with interval-valued intuitionistic multiplicative preference relations based on bounded confidence

This study proposes a consensus and consistency enhancing method considering bound confidence for Group Decision-Making (GDM) under interval-valued intuitionistic multiplicative (IVIM) context. First, aiming at the defect that the existing consistency definitions for IVIM preference relations (IVIMPRs) violate the invariance regarding arrangement of the compared objectives' labels, this study presents a new consistency definition for IVIMPRs. Then, based on the proposed new consistency definition for IVIMPRs, an optimization model is constructed to obtain the consistent IVIMPR. Meanwhile, a new consistency index of an IVIMPR is defined based on the distance between the IVIMPR and the set of consistent IVIMPRs. For the unacceptably consistent IVIMPR, an interactively iterative algorithm considering bounded confidence in its feedback adjustment process is presented to enhance its consistency level. As to GDM with IVIMPRs, an interactively iterative algorithm considering bounded confidence and individual consistency management in its feedback adjustment process is presented to enhance the consensus level among experts. After giving the concept of normalized interval-valued multiplicative priority weight vector, this study puts forward a new method to obtain the IVIM priority weight vector (IVIMPWV). Finally, the feasibility of the method is confirmed by a numerical example and a simulation analysis, and its superiorities are verified by some comparative analyses.