A new group decision-making approach is developed to address a multiple criteria sorting problem with uncertainty. The uncertainty in this paper refers to imprecise evaluations of alternatives with respect to the considered criteria. The belief structure and the evidential reasoning approach are employed to represent and aggregate the uncertain evaluations. In our approach, the preference information elicited from a group of decision makers is composed of the assignment examples of some reference alternatives. The disaggregation–aggregation paradigm is utilized to infer compatible preference models from these assignment examples. To help the group reach an agreement on the assignment of alternatives, we propose a consensus-reaching process. In this process, a consensus degree is defined to measure the agreement among the decision makers’ opinions. When the decision makers are not satisfied with the consensus degree, possible solutions are explored to help them adjust assignment examples in order to improve the consensus level. If the consensus degree arrives at a satisfactory level, a linear program is built to determine the collective assignment of alternatives. The application of the proposed approach to a customer satisfaction analysis is presented at the end of the paper. 
A group decision-making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty