For many years, supplier selection as an important multi-criteria decision has attracted both the researchers and practitioners. During recent years, high incidence of natural disasters, terrorism attacks, labor strikes and other kinds of risks, also known as disruptions, indicates the vulnerability of procurement process to these unpredicted events. In this study, a new framework is introduced to select suppliers while considering the supply risks. In the proposed framework, an expert determines the reliabilities of procurement elements (i.e., production, transportation and communication) based on some proposed risk factors. Then, a trained Multi-Layer Perceptron (MLP) network plays the role of the expert opinion for estimating the reliability scores. In addition to reliabilities, the Data Envelopment Analysis (DEA) is used to take into account the conventional selection criteria: price, delivery, quality and capacity. A set of Pareto-optimal suppliers is obtained from the combination of efficiencies and reliability scores. Finally, the decision maker chooses between the non-dominated suppliers. Obtained experiment results indicate the effectiveness of the proposed framework.