The interactive consensus reaching process with the minimum and uncertain cost in group decision making

The consensus model with the minimum cost (or minimum adjustments or minimum information loss) is a powerful decision tool for consensus building in the group decision making (GDM). In the extant consensus models with the minimum cost, the unit adjustment cost of each expert is assumed to be exactly known, and an optimization-based consensus model is utilized to support the consensus building. In the practical GDM, however, it is difficult to obtain the exact unit adjustment costs, and the unit adjustment costs of experts are often uncertain. Moreover, we argue that the consensus cannot be achieved directly using the established optimization-based consensus model, because the consensus building is an interactive process that needs the participation of experts. This paper proposes an interactive consensus reaching process with the minimum and uncertain cost. In the consensus reaching process, an optimization-based consensus model with the uncertain unit cost is constructed to obtain the optimal adjusted opinions of experts. Then, the costs/resources are provided for experts to modify their opinions, and the obtained optimal adjusted opinions are used as a reference for the opinions-modifying in the consensus reaching process. Meanwhile, the unit adjustment costs of experts can be estimated according to the actual situation of the opinions-modifying in the consensus reaching process. The detailed numerical and simulation analysis are conducted to demonstrate the validity of the proposed consensus reaching model.