In recent years, many fuzzy time series methods have been proposed in the literature. Some of these methods use the classical fuzzy set theory, which needs complex matricial operations in fuzzy time series methods. Because of this problem, many studies in the literature use fuzzy group relationship tables. Since the fuzzy relationship tables use order of fuzzy sets, the membership functions of fuzzy sets have not been taken into consideration. In this study, a new method that employs membership functions of fuzzy sets is proposed. The new method determines elements of fuzzy relation matrix based on genetic algorithms. The proposed method uses first-order fuzzy time series forecasting model, and it is applied to the several data sets. As a result of implementation, it is obtained that the proposed method outperforms some methods in the literature.