This paper presents an efficient and simplified type-1 and interval type-2 non singleton fuzzy logic systems (NSFLSs) in order to obviate time series forecasting problems. These methods have applied non singleton fuzzification by Sharp Gaussian membership function, logical inference with the First-Infer-Then-Aggregate (FITA) approach and parametric defuzzification. Rules are generated based on high order fuzzy time series. In interval type-2 FLS, which can better handle uncertainties, type-2 sets are generated, using fuzzy normal forms by applying Yager Parametric classes of operators. Moreover, in these systems, some elements such as membership functions, operators and length of intervals affect the forecasting results. In addition, a method for tuning parameters of fuzzy logic systems with genetic algorithm is presented. Finally, the proposed methods are applied to predict the temperature and the Taiwan Stock Exchange (TAIEX). The results show the higher degree of accuracy of the model compared to the previous methods.