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A fuzzy time series has been applied to the prediction of enrollment, temperature, stock indices, and other domains. Related studies mainly focus on three factors, namely, the partition of discourse, the content of forecasting rules, and the methods of defuzzification, all of which greatly influence the prediction accuracy of forecasting models. These studies use fixed analysis window sizes for forecasting. In this paper, an adaptive time-variant fuzzy-time-series forecasting model (ATVF) is proposed to improve forecasting accuracy. The proposed model automatically adapts the analysis window size of fuzzy time series based on the prediction accuracy in the training phase and uses heuristic rules to generate forecasting values in the testing phase. The performance of the ATVF model is tested using both simulated and actual time series including the enrollments at the University of Alabama, Tuscaloosa, and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX). The experiment results show that the proposed ATVF model achieves a significant improvement in forecasting accuracy as compared to other fuzzy-time-series forecasting models.