•A group decision making method with two different modes of assessments is developed.•Belief distributions and distributed preference relations are unified.•Internal consistency and Pareto principle for unifying the two modes are proven.•The proposed method is used to solve the problem of selecting a key field.•Internal consistency and Pareto principle are verified using the data in the problem. To solve multiple criteria group decision making (MCGDM) problems with belief distributions (BDs) and distributed preference relations (DPRs), this paper proposes a new method. For unifying BDs and DPRs, the transformation from BDs into DPRs is developed. Two important properties of the transformation, which are the internal consistency and the Pareto principle of social choice theory, are theoretically proven on the condition that the evidential reasoning algorithm is used to combine DPRs. With a view to relieving the burden on decision makers to provide complete DPR matrices, the process of generating solutions to the MCGDM problems from the DPRs between neighboring alternatives and belief matrices composed of BDs is presented through the consistency between the score intervals of the DPRs. The proposed method is used to select a key filed for an enterprise located in Hefei, Anhui Province, China. The selection is validated by analyzing actual situations to demonstrate the applicability and validity of the proposed method. The internal consistency and the Pareto principle of social choice theory are verified through the relevant results of conducting the selection and simulation experiments based on selected data and random parameters in the field selection problem.