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Forecasting activities are frequent and widespread in our life. Since Song and Chissom proposed the fuzzy time series in 1993, many previous studies have proposed variant fuzzy time series models to deal with uncertain and vague data. Two drawbacks of these models are that they do not consider information density of each interval, and assign appropriate weights of fuzzy relations. This paper proposes a new method to determine the length of intervals according to the N-th Quantile Discretization Approach (NQDA). It calculates the cut-points by computing observations quantity of each interval. Besides, the concept of determining feasible weights for fuzzy relations by cardinality is also adopted in this paper. The yearly data on enrollments at the University of Alabama and Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) are adopted to verify and evaluate the performance of the proposed method. The forecasting accuracies of the proposed method are better than other methods.