Sustainable supply chain management has received much attention from both academia and industry due to various issues such as economic stability, environment conservation, and social ethics. To improve the sustainable performance of a value chain, its members need to carefully select their suppliers in relation to their own strategy. Thus, an effective tool for sustainable supplier selection and evaluation is essential, which considers the triple bottom line (TBL) of economic, environmental and social aspects by means of criteria adapted to the situation analysed. This paper develops a fuzzy decision tool to evaluate the sustainable performance of suppliers according to TBL. Sustainability criteria are identified to take into account the real hotspots in a food value chain. The proposed model integrates triangular fuzzy numbers (TEN), AHP (Analytic Hierarchy Process) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) in a novel way to consider quantitative and qualitative criteria as well as objective and subjective data. This is missing in most existing research when building their fuzzy models for supplier selection, but critical in dealing with the heterogeneous data available for TBL assessment. The application in a sustainable agrifood value chain illustrates the effectiveness of the proposed tool.