In literature, several fuzzy time series models are proposed to obtain better forecasting performance. Although the shape of membership functions has an important effect on the forecasting performance, piecewise crisp membership functions are used in all of these models without showing any plausible reason. Therefore, the forecasting is performed by using interval arithmetic operations instead of fuzzy inference. In this study, a new fuzzy time series model is proposed. In this model, triangular and trapezoidal membership functions are used instead of classical piecewise crisp membership functions and the forecasting is performed by using Mamdani-type fuzzy inference with centroid defuzzification. The validation and effectiveness of the proposed model is shown through the example on the forecast of the enrollments of the University of Alabama. The results show that the proposed model has smaller forecasting mean square error value than two main time series models.