Distributionally Robust Chance Constrained Maximum Expert Consensus Model with Incomplete Information on Uncertain Cost

The maximum expert consensus model (MECM) with uncertain cost is a prominent area of research in group decision-making (GDM). The typical approach to addressing uncertain costs involves either possessing detailed information about its distribution or ensuring that the result is optimal under worst-case cost scenarios. In this paper, we assume that the probability of meeting the total uncertain consensus cost is not less than a given threshold at a specified level of confidence. Only the first- and second-order moments and the support of uncertain costs are used to construct the ambiguous probability distribution set. Building on distributionally robust optimization (DRO), we propose a novel distributionally robust chance-constrained MECM (DRCC-MECM) with incomplete information on uncertain costs. Additionally, by approximating the total uncertain consensus cost chance constraint with a worst-case conditional value-at-risk (CVaR) constraint, the DRCC-MECMs with different aggregation operators are transformed into tractable semi-definite programming models. Finally, the efficacy and advantages of the proposed models are demonstrated through an application to transboundary water pollution control in China. Sensitivity and comparative analyses further underscore the effectiveness of the proposed models in addressing uncertain costs in this context.