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

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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

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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)

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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

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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)

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

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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 A A A A A3 …

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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

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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

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

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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

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

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

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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%

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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 , Q. Song and B.S. Chissom, “Forecasting enrollments with fuzzy time series – part 1”, Fuzzy Sets and Systems, vol. 54, pp. 1-9, Q. Song and B.S. Chissom, “Forecasting enrollments with fuzzy time series – part 2”, Fuzzy Sets and Systems, vol. 62, pp. 1-8, S.-M. Chen, “Forecasting Enrollments Based on Fuzzy Time Series”, Fuzzy Sets and Systems, vol. 81, pp , S.-M. Chen, “Temperature Prediction using Fuzzy Time Series”, IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, vol. 30, pp , K.Huarng, “Heuristic Models of Fuzzy Time Series for Forecasting”, Fuzzy Sets and Systems, vol. 123, pp , 2001.

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Thank you for attention! Do you have any Questions?

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