Supply chain management is taken into account as an inseparable component in satisfying customers' requirements.This paper deals with the distribution network design (DND) problem which is a critical issue in achieving supply chain accomplishments. A capable DND can guarantee the success of the entire network performance. However, there are many factors that can cause fluctuations in input data determining market treatment, with respect to short-term planning, on the one hand. On the other hand, network performance may be threatened by the changes that take place within practicing periods, with respect to long-term planning. Thus, in order to bring both kinds of changes under control, we considered a new multi-period, multi-commodity, multi-source DND problem in circumstances where the network encounters uncertain demands. The fuzzy logic is applied here as an efficient tool for controlling the potential customers' demand risk. The defuzzifying framework leads the practitioners and decision-makers to interact with the solution procedure continuously. The fuzzy model is then validated by a sensitivity analysis test, and a typical problem is solved in order to illustrate the implementation steps. Finally, the formulation is tested by some different-sized problems to show its total performance.