Consensus adjustment for multi-attribute group decision making based on cross-allocation

Consensus adjustment is crucial in group decision making (GDM), aiming to reduce discrepancies in decision makers’ (DMs’) judgments for final decision results. The consensus adjustments made by DMs are interactive rather than independent. However, few studies investigate the consensus adjustment problem from the perspective of interactions among DMs. This study first constructs a model to determine the total minimum consensus adjustment under the requirements of consensus threshold and individual-collective judgment bias. Then, a consensus adjustment approach based on cross-allocation scheme is proposed to address the inconsistency between individual and collective minimum adjustments, which concerns all DMs’ individual favorable allocation results under the total minimum consensus adjustment. The cross-allocation scheme ensures unanimous support for the same allocation result among all rational DMs, thereby eliminating the discrepancies among them. Subsequently, the optimization model-based minimum consensus judgment penalty is formulated to handle the non-cooperative behaviors of DMs. Furthermore, we show how to determine the unique consensus adjustment result for the non-cooperative DMs using the cross-allocation scheme. Therefore, our study contributes by developing a new GDM method that conducts consensus adjustment allocation by considering interactions among DMs. Finally, a case study is employed to demonstrate the specific application of the new method and discuss its efficiency. Meanwhile, comparison analysis and simulation experiments are provided.