This study presents a quantitative methodology for Floating Photovoltaic (FPV) power plant site selection in Turkey using Geographical Information Systems (GIS) and fuzzy sets, which is one of the Multi-Criteria Decision Making (MCDM) methods. In this study, we propose a new hybrid framework which combines fuzzy rough number (FRN) based decision making model including LAAW (Logarithmic Additive Assessment of the Weight coefficients) and RAFSI (Ranking of Alternatives through Functional mapping of criterion subintervals into a Single Interval). The fuzzy rough number is applied for handling the uncertainty and inaccuracy of experts’ opinions in the evaluation process. Firstly, FRN based LAAW method is used to determine the weighting coefficients of the criteria. Secondly, FRN based RAFSI method is used to rank the alternatives. The proposed decision making model is applied to determine feasible site for Floating Photovoltaic (FPV) system in Southern part of Turkey. Out of the five alternative sites, Manavgat - Antalya is concluded to be the most suitable site, and the second-best alternative is Göksun - Karaman. The results show the rationality and applicability of the proposed model.