A drawback of existing fuzzy forecasting methods based on fuzzy time series is that they use the first-order fuzzy time series to deal with forecasting problems in which the forecasting results are not good enough. Using a high-order fuzzy time series to deal with fuzzy forecasting problems can overcome this drawback. In this paper, we propose a new fuzzy time series model called the high-order fuzzy time series model to deal with forecasting problems. Based on the proposed model, we develop an algorithm to forecast the enrollments of the University of Alabama, where the historical enrollment data at the University of Alabama (Song and Chissom 1993a, 1994) are used to illustrate the forecasting process. The forecasting accuracy of the proposed method is better than that of the existing methods.

A drawback of traditional forecasting methods is that they can not deal with forecasting problems in which the historical data are represented by linguistic values. Using fuzzy time series to deal with forecasting problems can overcome this drawback. In this paper, we propose a new fuzzy time series model called the two-factors time-variant fuzzy time series model to deal with forecasting problems. Based on the proposed model, we develop two algorithms for temperature prediction. Both algorithms have the advantage of obtaining good forecasting results.