The robust maximum expert consensus model considering satisfaction preference

In the consensus-reaching process (CRP), decision makers (DMs) tend to consider their satisfaction with opinions when adjusting their viewpoints, which may influence the number of DMs that can reach consensus in the actual decision. However, in the study of the maximum expert consensus model (MECM), the personal satisfaction of experts is rarely considered. To address this gap, this paper introduces a novel satisfaction degree function into the MECM, termed the maximum expert consensus model with satisfaction (MECM-S). Given the uncertainty surrounding adjustment costs, this study further explores three distinct uncertainty scenarios and proposes a robust MECM-S (RMECM-S) to manage the uncertainty of opinion adjustment costs in the decision-making process. Additionally, to overcome the limitations of existing consensus-reaching mechanisms, this paper proposes a new consensus degree function, which is integrated into the proposed model to develop a soft consensus RMECM-S (soft-RMECM-S). The proposed models were validated through their application to the Taihu Lake water pollution control negotiation, and a sensitivity analysis was conducted to assess their effectiveness. The findings demonstrate that incorporating individual satisfaction and handling cost uncertainty significantly enhance the feasibility and reliability of the consensus-reaching process, contributing to more effective decision-making in complex scenarios.