"Most of these studies are based on the assumptions that the weights of a criterion are represented by the known crisp numbers.. However, there exist little investigation on multi-attribute decision-making problems with both ratings of green suppliers on criteria and weights being expressed with fuzzy sets .. Thus, an interesting and important issue is how to utilize the unknown weights information of a criterion to select the most desirable green supplier.. Consequently, it is beneficial to combine the advantages of picture fuzzy sets in representing information and the superiority of fractional programming."