Fuzzy time series models have many applications in forecasting, especially in the economic forecast. In recent years many works have been completed towards improving accuracy and reducing the amount calculated in fuzzy time series models such as the article by Chen and Hsu, Huarng, Kuo, Wu... Most methods are based on the technique of fuzzy logical relationship groups (Chen [4]) to reduce the amount of computation. However, the fuzzy logical relationship groups are used without attention to their order of appearance and the occurrences of the components in the right side of the fuzzy logical relationship groups. From this remark, the authors propose fuzzy logical relationship groups depends on temporal order. Thanks to the concept of time dependent fuzzy logical relationship groups and using the weighted fuzzy time series model, the authors have established an effective algorithm for predicting time series. The new model is applied for enrollments forecasting of the University of Alabama. The obtained peforments shows that the proposed method give better accuracy than Chen and Yu models.