For many years, supplier selection as an important multi-criteria decision has attracted both the researchers and practitioners. Recently, high incidences of natural disasters, terrorism attacks, labor strikes, and other kinds of risks, also known as disruptions, indicate 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 is asked to determine the reliability of each procurement element (i.e., production, transportation, and communication) based on some proposed risk factors. Then, a distinct Multi-Layer Perceptron (MLP) network is trained to play the role of the expert opinion for estimating the reliability scores of each procurement. 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 is recommended to choose between the non-dominated suppliers. Obtained experiment results indicate the effectiveness of the proposed framework.