Effective intervals determined by information granules to improve forecasting in fuzzy time series

• Partitioning the universe of discourse into intervals with unequal length.
• Determining intervals by information granule.
• These intervals carry well-defined semantics.
• The proposed method is very robust and stable to forecast in fuzzy time series.

Partitioning the universe of discourse and determining effective intervals are critical for forecasting in fuzzy time series. Equal length intervals used in most existing literatures are convenient but subjective to partition the universe of discourse. In this paper, we study how to partition the universe of discourse into intervals with unequal length to improve forecasting quality. First, we calculate the prototypes of data using fuzzy clustering, then form some subsets according to the prototypes. An unequal length partitioning method is proposed. We show that these intervals carry well-defined semantics. To verify the suitability and effectiveness of the approach, we apply the proposed method to forecast enrollment of students of Alabama University and Germany’s DAX stock index monthly values. Empirical results show that the unequal length partitioning can greatly improve forecast accuracy. Further more, the proposed method is very robust and stable for forecasting in fuzzy time series.