A robust data-driven maximum experts consensus modeling approach considering fairness concerns under uncertain contexts

Due to the uncertainty of information, decision-makers within a group often seek to compare themselves with others to determine whether they are being treated fairly, which introduces significant instability into consensus management. To provide a reliable solution, this study aims to achieve fair consensus in uncertain environments. First, fairness concerns are incorporated into the maximum experts consensus model, measuring decision-makers’ fairness utility levels and revealing the relationship between their opinion adjustment behavior and fair consensus. Additionally, to more accurately and objectively characterize the uncertainty of consensus parameters, we use a kernel estimation method based on historical decision data to capture the uncertain features of both costs and opinions separately, thereby analyzing their impact on fair consensus. Robust optimization methods are then employed to mitigate the decision risks associated with these uncertainties, and various robust data-driven consensus models are constructed. These models not only eliminates the decision risks arising from uncertainty, but also addresses the issue of conservative consensus often encountered in traditional experience-driven robust optimization to some extent. We also developed an improved particle swarm optimization algorithm to solve the robust models. Finally, extensive numerical analysis results demonstrate that our approach produces more stable and reliable decision outcomes.