Supplier selection is a strategic decision for reducing risk, maximising overall value, and establishing strong, mutually beneficial long-term relationships between the members in supply chain management. Identifying and prioritising the risks and benefits from each supplier enables managers to consider these factors and select the most suitable supplier. We propose an integrated approach for supply chain risk-benefit assessment and supplier selection by combining the fuzzy analytic hierarchy process (AHP) with the fuzzy multiplicative multi-objective optimisation based on ratio analysis (MULTIMOORA). The fuzzy AHP is used to measure the importance of the supply chain risks and benefits and the fuzzy MULTIMOORA is used to rank the suppliers. We present a case study to demonstrate the applicability and exhibit the efficacy of the proposed integrated framework. We also study the uncertainty in the output of our proposed framework using sensitivity analysis.