The integration of sustainable indicators into supply-chain management (SCM), including cost, innovation capability, quality, service capability, long-term cooperation, environmental management system, pollution reduction, green image, social responsibility, and employment practices, has become essential for conducting strategic analyses of the entire supply-chain process competitive advantage. This study proposes a fuzzy integration multi-criteria decision-making (MCDM) method to solve SCM issues. To navigate this complexity, a multi-criterion decision-making (MCDM) framework is employed, integrating MCDM methods with fuzzy logic to effectively address subjective environmental criteria. This innovative approach not only enhances supply-chain management (SCM) but also emphasizes the necessity for ongoing innovation in tackling contemporary supply-chain challenges. It serves as a cornerstone for sustainable supplier selection practices and optimizing SCM processes. In this study, a hybrid fuzzy MCDM method is proposed for supplier selection. The method addresses supplier selection by utilizing evaluations from expert decision-makers based on predetermined criteria. This comprehensive approach ensures that all relevant factors are considered, promoting sustainable and efficient supply-chain management.