In deterministic DEA models, precise values are assigned to input and output data while they are intrinsically subjected to some degree of uncertainty. Most studies in this area are based on the assumption that inputs and outputs are equipped with some pre-known knowledge that enables one to use probability theory or fuzzy theory. In the lack of such data, one has to trust on the experts’ opinions, which can be considered as a sort of uncertainty. In this situation, the axiomatic approach of uncertainty theory initiated by Liu (Uncertainty theory. Berlin: Springer, 2007) could be an adequate powerful tool. Applying this theory, Wen et al. (J Appl Math, 2014; Soft Comput 1987–1996, 2015) suggested an uncertain DEA model while it has the disadvantage of pessimism. In this paper, we introduce another uncertain DEA model with the objective of acquiring the highest belief degree that the evaluated DMU is efficient. We also apply this model in ranking of the evaluated DMUs. Implementation of the model on different illustrative examples reveals that the ranks of DMUs are almost-stable in our model. This observation states that the rank of a DMU may roughly alternate with respect to the variation of minimum belief degrees. Our proposed model also compensates the rather optimistic point of view in the Wen et al. model that identifies all DMUs as efficient for higher belief degrees.