An Altruism-Based Multi-Criteria Group Decision-Making Model under Uncertain Environment: A Distributionally Robust Consensus Reaching Method

In consensus reaching for multi-criteria group decision making (MCGDM), existing studies commonly address uncertainty in decision makers’ unit adjustment costs by adopting robust optimization (RO) methods, which typically rely on predefined uncertainty sets and focus on worst-case scenarios. However, in practice the probability distribution of adjustment costs is difficult to specify accurately due to psychological and environmental influences. Moreover, social behavioral preferences such as altruism, are rarely incorporated into the consensus process. To overcome these limitations, this paper proposes an altruism-based multi-criteria group decision-making model with uncertain costs by using a distributionally robust consensus reaching method (DRO-MCGDM). First, an altruistic utility function is introduced to capture the trade-off between individual self-interest and the welfare of others, thereby reflecting social interaction behaviors among decision makers. Second, instead of assuming exact distributional information, the distributionally robust optimization (DRO) framework is employed to model uncertainty in unit adjustment costs by constructing an ambiguity set based on partial distributional information. Through duality theory, the proposed model is reformulated into a tractable distributionally robust equivalent form. Finally, the model is applied to a power resource allocation problem, and its effectiveness is verified through sensitivity and comparative analyses.