The theory of Ambiguous Fuzzy Set (AFS) especially termed as single-valued ambiguous set (SVAS) proved as a powerful tool to deal with uncertain information. Choosing the best renewable energy source (RES) is a complex multi-criteria decision-making process because of the many factors to consider. In this study, the TOPSIS method is suggested under the SVAS environment. Then, this method is applied to the selection of RESs through the case study. The obtained results, are compared with some of the existing studies to validate the proposed results. The novelty of this studies lies that: the TOPSIS method in the domain of SVAN which is not covered in the existing literature so far is presented; and then to practically implement the TOPSIS method, a hydroelectric power RESs selection is considered and applied; the comparative result validates the obtained results from the proposed TOPSIS method obtained in the domain of SVAN.