Robust minimum cost consensus models with uncertain modification behavior in group decision making
针对群体决策中决策者修改行为的不确定性，提出了基于合作度的最小成本共识模型及其鲁棒版本，通过数值实验分析了不确定性水平和共识阈值对成本的影响。
In group decision making, achieving consensus is critical for ensuring both the quality and practical implementation of the final group solution. The interaction between the moderator and decision makers (DMs) plays a pivotal role in reaching group consensus, often involving a costly negotiation process fraught with uncertainty. Most existing consensus studies focus either on the moderator’s or DMs’ perspective, neglecting DMs’ potential modification behaviours or unrealistically assuming full acceptance of the moderator’s suggestions. While in practice, DMs’ responses vary due to factors such as personal motivations and private considerations, which are hard to quantify. This study aims to develop robust minimum cost consensus models that manage the uncertainty of DMs’ modification behaviours to ensure group consensus. First, we introduce the concept of cooperation degree and develop the cooperation degree-based minimum cost consensus model (CDMCCM), which is further extended to the weighted CDMCCM (WCDMCCM) by incorporating a weighted averaging operator. To address the uncertainty inherent in the cooperation degree, we develop robust versions of both the CDMCCM and WCDMCCM using uncertain sets in the form of box, ellipsoid, and polyhedron. Finally, numerical results show that as the uncertainty level increases or the consensus threshold decreases, the minimum consensus cost rise, with the box uncertainty set consistently incurring the highest cost.