Traditional stochastic inventory models assume to have complete knowledge about the demand probability distribution. However, in reality it is often difficult to characterize demand precisely, especially with limited historical data or through subjective forecasting. In this paper, we aim to develop a consistent framework of formulating demand uncertainties in single-period (newsvendor) problems, where a set of discrete assessment grades and/or grade intervals are used to represent complex uncertainties in both quantitative and qualitative evaluations. In this uncertainty formulation framework, we use random set theory to study optimal ordering policies for the newsvendor problem under optimistic, pessimistic, minimum regret and maximum entropy criteria respectively. Numerical studies are conducted to illustrate the effectiveness of the proposed approach.