Supplier selection has long been regarded as one of the most challenging issues in supply chain optimization, and a firm's success largely depends on choosing an appropriate supplier. The supplier selection process is a highly complex, multi-person, group decision-making problem that can benefit from systematic, rational approaches to improve the evaluation of priorities. This process typically relies on collective input from individuals across different functional areas within an organization. This study demonstrates how the Fuzzy Analytic Hierarchy Process (F-AHP) can be effectively integrated with the Failure Mode and Effects Analysis (FMEA) approach to select the best supplier in a supply chain risk environment. The F-AHP method is employed to determine the relative weight of each criterion, while the FMEA technique is used to calculate the Risk Priority Number (RPN) for each criterion and its associated sub-criteria in the supplier selection problem. Sobhan Pharmaceutical company is selected as a case study to implement the proposed approach, and the results indicate improvements in performance across various criteria.