Consensus Building for Uncertain Large-Scale Group Decision-Making Based on the Clustering Algorithm and Robust Discrete Optimization

Consensus reaching processes (CRPs) including the feedback adjustment mechanism generally require extended periods of time to bridge the opinion gap among decision makers. Therefore, minimum cost consensus (MCC) problems with known adjustment costs have been widely reported. However, the exact unit adjustment costs are difficult to obtain through practical CRPs. To solve these problems, this paper proposes a novel CRP framework for uncertain large-scale group decision-making based on robust discrete optimization. First, an enhanced iterative self-organizing data analysis technique algorithm is provided to dynamically cluster decision makers together in small subgroups under interval opinions. Second, to establish the optimization-based consensus rules in the feedback process, an MCC integer optimization model is established to minimize the total consensus costs in consensus reaching. Furthermore, with the indeterminate unit adjusting costs, a robust discrete MCC optimization model is constructed, which can control the degree of conservatism of the optimal consensus opinion and compute the optimal modified opinions of decision makers. Finally, a case study and comparative analysis indicate the effectiveness and superiority of the proposed CRP method and that the robust discrete MCC model has stronger robustness in the uncertain decision environment.