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. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series2 Overview  Introduction  Fuzzy Time Series  Forecasting Enrollments with a new Time- Invariant Fuzzy Time Series method  Forecasting Results and Discussion  Conclusion  References

3. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series3 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)

4. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series4 Fuzzy Time Series  First-order fuzzy time series  Fuzzy Logical Relationship ;  Forecasting is an operator

5. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series5 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 variables of 6 fuzzy sets as, …. (big decrease), (decrease), (no change), (increase), (big increase), (too big increase)

6. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series6 Fuzzified variations of University of Alabama enrollment

7. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series7 A New method of Time-Invariant Fuzzy Time Series (Cont.)  First-order fuzzy logical relationships: Years Fuzzified Variations 1972 A4 1973 A4 1974 A5 1975 A5 1976 A3 …

8. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series8 A New method of Time-Invariant Fuzzy Time Series (Cont.)  Group fuzzy logical relationships:  - union of relationships in each group

9. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series9 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

10. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series10 Forecasted Outputs and Actual Enrollments from 1973-1993

11. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series11 Results and Discussion  The proposed method is implemented in MATLAB

12. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series12 Results and Discussion (Cont.)

13. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series13 Results and Discussion (Cont.)  Different number of fuzzy sets:

14. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series14 Conclusion  Sorely available historical data used for forecasting  Significantly improves accuracy  For all examined cases (different number of fuzzy sets) forecasting error below 3%

15. Melike Şah, Konstantin Y. Degtiarev Forecasting Enrollment Model Based on First-Order Fuzzy Time series15 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.

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