Robust minimum cost consensus modeling with consensus principle and tolerance level for group decision making

Group decision making (GDM) involves adjusting individual opinions to reach a consensus outcome, which requires considering both the decision goals and coordination mechanisms. The minimum cost consensus model (MCCM) is a commonly used approach for promoting consensus, but previous studies have primarily focused on improving consensus efficiency and quality, neglecting the impact of uncertainty and decision risks. To address this issue, in this paper, we propose a robust optimization (RO) method that incorporates uncertainty to obtain consensus results, reducing risks associated with cost uncertainty. Four types of uncertainty sets are constructed under classical RO to describe the uncertainty in unit adjustment costs. The data-driven RO utilizing historical data is also introduced to alleviate the over-conservatism of classical robust models which contain extreme but rarely occurring scenarios. Our proposed robust MCCM integrates consensus principle and tolerance level under cost uncertainty. We apply the proposed models to solve the emission rights negotiation problem, and the results demonstrate their distinct advantages in risk avoidance and model robustness. Decision makers (DMs) and moderators can select different RO models with varying risk levels, tailored to their risk preferences and specific situations.