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Forecasting Enrollment Model Based on First-Order Fuzzy Time Series

Forecasting Enrollment Model Based on First-Order Fuzzy Time Series. By Melike Şah ( * ) Konstantin Y. Degtiarev İ nternational Conference on Computational İ ntelligence ( İ CC İ ) 17-19 December 2004, İ stanbul, Turkey. Overview. Introduction Fuzzy Time Series

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Forecasting Enrollment Model Based on First-Order Fuzzy Time Series

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  1. Forecasting Enrollment Model Based on First-Order Fuzzy Time Series By Melike Şah (*) Konstantin Y.Degtiarev İnternational Conference on Computational İntelligence (İCCİ) 17-19 December 2004, İstanbul, Turkey

  2. Overview • Introduction • Fuzzy Time Series • Forecasting Enrollments with a new Time-Invariant Fuzzy Time Series method • Forecasting Results and Discussion • Conclusion • References Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  3. Introduction • Forecasting: weather, staff scheduling, finance • Well-known forecasting methods cannot solve problems, when data are available in linguistic form • A new Time-Invariant Fuzzy Time Series method to forecast University of Alabama enrollment • The effect of different number of fuzzy sets • Comparison with Song&Chissom and Chen’s time invariant-methods (see Reference section, slide 15) Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  4. Fuzzy Time Series • First-order fuzzy time series • Fuzzy Logical Relationship • ; • Forecasting is an operator Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  5. A New method of Time-Invariant Fuzzy Time Series • Variations of University of Alabama enrollment • At fuzzification stage different number of fuzzy sets [5-9] used. Intervals and linguistic variablesof 6 fuzzy sets as • , …. • (big decrease), (decrease), (no change), (increase), (big increase), (too big increase) Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  6. Fuzzified variations of University of Alabama enrollment Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  7. A New method of Time-Invariant Fuzzy Time Series (Cont.) • First-order fuzzy logical relationships: Years Fuzzified Variations 1972 A4 • A4 • A5 • A5 • A3 … … Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  8. A New method of Time-Invariant Fuzzy Time Series (Cont.) • Group fuzzy logical relationships: • - union of relationships in each group Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  9. A New method of Time-Invariant Fuzzy Time Series (Cont.) • Forecasting: • Deffuzification: • If MF all 0  forecasted variation is 0 • If MF has one Max midpoint of that interval • If MF has two or more consecutive Maxs  Midpoint of corresponding conjunct intervals • Otherwise  Centroid of the output Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  10. Forecasted Outputs and Actual Enrollments from 1973-1993 Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  11. Results and Discussion • The proposed method is implemented in MATLAB Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  12. Results and Discussion (Cont.) Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  13. Results and Discussion (Cont.) • Different number of fuzzy sets: Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  14. Conclusion • Sorely available historical data used for forecasting • Significantly improves accuracy • For all examined cases (different number of fuzzy sets) forecasting error below 3% Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  15. References • Q. Song and B.S. Chissom, “Fuzzy time series and its models”, Fuzzy Sets and Systems, vol. 54, pp. 269-277, 1993. • Q. Song and B.S. Chissom, “Forecasting enrollments with fuzzy time series – part 1”, Fuzzy Sets and Systems, vol. 54, pp. 1-9, 1993. • Q. Song and B.S. Chissom, “Forecasting enrollments with fuzzy time series – part 2”, Fuzzy Sets and Systems, vol. 62, pp. 1-8, 1994. • S.-M. Chen, “Forecasting Enrollments Based on Fuzzy Time Series”, Fuzzy Sets and Systems, vol. 81, pp. 311-319, 1996. • S.-M. Chen, “Temperature Prediction using Fuzzy Time Series”, IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, vol. 30, pp. 263-275, 2000. • K.Huarng, “Heuristic Models of Fuzzy Time Series for Forecasting”, Fuzzy Sets and Systems, vol. 123, pp. 369-386, 2001. Forecasting Enrollment Model Based on First-Order Fuzzy Time series

  16. Thank you for attention! Do you have any Questions?

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