A group decision making model for partially ordered preference under uncertainty

• Unified belief structure to represent the partially ordered preferences with belief degrees.
• Transformation of typical preference representation models into panoramic belief structure.
• Evidential reasoning based approach to combine the partially ordered preferences with belief degrees.

In many decision making problems, the experts are not able to provide accurate preferences among the alternatives but some kind of partial orders with certain belief degrees, due to limited expertise related to the problem domain, lack of data, or time restriction and so on. To facilitate decision making in this type of situations, this paper proposes a belief structure to represent the partially ordered preferences with belief degrees, which can cover both qualitative and quantitative aspects of the evaluation and can also represent indifference and incomparability relations as well. An evidential reasoning based preference combination approach is then applied to combine the partially ordered preferences with belief degrees of the experts. The collective ordering of alternatives, which again could be a partial order, is generated based on a distance measure between pairs of preference relations. A group decision making model based on the preference combination and the collective ordering generation is then established for partially ordered preference under uncertainty. Numerical examples are provided to illustrate the rationality and effectiveness of the proposed approach.