"Sustainability" term has not only become increasingly important globally for individual companies, but also become important for whole supply chains. The selection of supplier is a significant decision for the sustainability of supply chains. Literature review revealed that supplier selection is made traditionally based on economic attributes which are insufficient for sustainability of supply chains as sustainability requires taking economic, environmental, and social issues into account. For this purpose, this paper proposes determining the green supplier selection attributes and then developing a methodology for assessment and ranking of green suppliers based on determined attributes. The first contribution of this study is to propose a novel method, which is FROV (fuzzy extension of range of value) to literature. The latter is to utilize fuzzy extension of preference selection index (FPSI) to identify the weights of attributes. The third is to develop a novel fuzzy multiattribute decision-making model consisting of FPSI and FROV to determine the best supplier for a Turkish textile company.