1. Cairo University Institute of Statistical Studies and Research Department of Computer and Information Sciences A Novel Forecasting Fuzzy Time Series Model Ashraf K. Abd Elaal a, Hesham A. Hefny b, Ashraf H. Abd Elwahab c a Department of Computer and Information Sciences, The High Institute of Computer Science, Al-Kawser city at Sohag, Egypt. b Department of Computer and Information Sciences, Institute of Statistical Studies and Research, Cairo University, Egypt. c Department of Computer and Information Sciences, Electronics Research Institute, National Center for Research, Egypt. November 2009

2. Outlines 1- Introduction 2- Fuzzy Time Series Vs Traditional Time Series forecasting 3- Fuzzy Approaches of Forecasting 4- Proposed Model 5- Comparisons The Forecasting Results for Different Models 6- Conclusion 7- References

3. 1- Introduction Forecasting play an important role in our daily life. It is impossible to make a one hundred percent forecast, but researchers can do their best to increase the accuracy of forecasts. Traditional forecasting methods can deal with many forecasting cases, but they cannot solve forecasting problems in which the historical data are linguistic values. Fuzzy time series can solve forecasting problems in which the historical data are linguistic values.

4. 2- Fuzzy Time Series Vs Traditional Time Series forecasting The traditional forecasting methods fail to forecast the data with linguistic facts. Time series analysis often requires to turn a non-stationary series into a stationary series. The traditional time series requires more historical data along with some assumptions like normality postulates. The fuzzy forecasting methods success to forecast the data with linguistic facts. Fuzzy time series do not need to turn a non-stationary series into a stationary series and do not require more historical data along with some assumptions like normality postulates

5. 3- Fuzzy Approaches of Forecasting [Song and Chissom, 1993] presented the concept of fuzzy time series based on the historical enrollments of the University of Alabama. Fuzzy time series used to handle forecasting problems. Fuzzy time series deal with data without any assumptions like normality, and not requires data normalization, training set and the test set. It works with scant historical data

6. [Song and Chissom, 1993] [Song and Chissom, 1993] presented the time-invariant fuzzy time series model and the time-variant fuzzy time series model based on the fuzzy set theory for forecasting the enrollments of the University of Alabama. They presented a methodology for establish fuzzy time series, most of authors in fuzzy time series field took the same path, but they differ in some steps.

7. [Song and Chissom, 1993] The same steps of the methodology are:- 1- Define the universe of discourse U. U=[Dmin – D1, Dmax + D2] where, Dmin is the minimum value, Dmax is the maximum value, D1, D2 is the positive real numbers to divide the U into n equal length intervals. 2- Partition universal of discourse U into equal intervals.

8. [Song and Chissom, 1993] 4- Fuzzify the historical data. 5- Build fuzzy logic relationships. 3- Define the linguistic terms:-

9. [Song and Chissom, 1993]

10. 4- Proposed Model 1- cluster data into c clusters. 2- Determine membership values for each cluster. 3- Rank each cluster. 4- Define the Universe of Discourse U. U=[Dmin – D1, Dmax + D2] Where, Dmin is the minimum value, Dmax is the maximum value, D1, D2 is the positive real numbers to divide the U into n equal length intervals. 5- Partition universal of discourse U into equal intervals. 6- Fuzzify the historical data. 7- Build fuzzy logic relationships. 8- Calculate forecasted outputs:- if X i belong to Y s forecast(t)= Y s else if X j belong Y i,Y k,.. Forecast(t)=midpoint( these intervals) Where X: actual value, Y: cluster value.

11. 4- Proposed Model

12. 5- Comparisons The Forecasting Results for Different Models Year Actual enrollments Jilani 2008Tsaur 2005Yu 2005Chen 2008Cheng 2008Proposed 197113055135051360413660 13159 197213563135051360413660 1424213159 1973138671387314446 144841424213729 1974146961443515570 143391424214700 1975154601556015851158101936715474.315708 1976153111556015851158102444515474.315708 1977156031556015851158102502515474.315708 1978158611612215008155702010615474.316316 1979168071650216412163561701016146.516832 1980169191650216412163561841216988.316832 1981163881612215008155701753616988.316316 1982130551350513604136601667816146.513159 1983135631350513604136601771615474.313159 1984138671387314446 1448415474.313729 1985146961443515570 1433915474.314700 1986154601556015851158101936715474.315708 1987153111556015851158102444516146.515708 1988156031556015851158102502516988.315708 198915861161221500815570201061914416316 199016807165021641216356170101914416832 199116919165021641216356184121914416832 199216388161221641215570175361914416316 NRMSE0.0170.0390.0350.2950.0980.015

13. 5- Comparisons The Forecasting Results for Different Models

14. 6- Conclusion A novel fuzzy time series method based on fuzzy clustering has been proposed. The method of FCMI is integrated in the processes of fuzzy time series to partition datasets. Experimental results on enrollments at the University of Alabama and the comparison with other models: [Jilani and Burney, 2008], [Tsaur, Yang et al. 2005], [Yu-2, 2005], [Chen, Cheng et al. 2008], [Cheng, Wang et al. 2008] show from results that the proposed model is a good model for forecasting values.

15. 7- References 1- [Chen, T.-L., C.-H. Cheng, et al., 2008] Chen, T.-L., C.-H. Cheng, et al., "High-order fuzzy time-series based on multi-period adaptation model for forecasting stock markets", PhysicaA. 387 876–888, 2008. 2- [Cheng, C.-H., J.-W. Wang, et al., 2008] Cheng, C.-H., J.-W. Wang, et al., "Multi-attribute fuzzy time series method based on fuzzy clustering", Expert Systems with Applications. 34: 1235–1242, 2008. 3- [Friedman, M. and A. Kandel, 1999] Friedman, M. and A. Kandel, "Introduction to pattern recognition statistical, structural, neural and fuzzy logic approaches", London, Imperial college press, 1999. 4- [Huarng, K., 2001] Huarng, K., "Effective lengths of intervals to improve forecasting in fuzzy time series", Fuzzy Sets and Systems. 123 387–394, 2001. 5- [Jilani, T. A. and S. M. A. Burney, 2008] Jilani, T. A. and S. M. A. Burney, "Multivariate stochastic fuzzy forecasting models", Expert Systems with Applications. 35: 691–700, 2008. 6- [Kirchgässner, G. and JürgenWolters, 2007] Kirchgässner, G. and JürgenWolters, "Introduction to modern time series analysis", Berlin, Germany, Springer-Verlag, 2007. 7- [Liu, H.-T., 2007] Liu, H.-T., "An improved fuzzy time series forecasting method using trapezoidal fuzzy numbers", Fuzzy Optimization and Decision Making 6(1): 63-80, 2007. 8- [Palit, A. K. and D. Popovic, 2005] Palit, A. K. and D. Popovic, "Computational intelligence in time series forecasting theory and engineering applications", London, UK, Springer- Verlag, 2005. 9- [Song, Q. and B. S. Chissom-1, 1993] Song, Q. and B. S. Chissom, "Forecasting enrollments with fuzzy time series. I", Fuzzy sets and systems 54(1): 1-9, 1993. 10- [Song, Q. and B. S. Chissom-2, 1993] Song, Q. and B. S. Chissom, "New models for forecasting enrollments: fuzzy time series and neural network approaches", eric.ed.gov, 27 DOI: 1993. 11- [Tsaur, R.-C., J.-C. Yang, et al., 2005] Tsaur, R.-C., J.-C. Yang, et al., "Fuzzy relation analysis in fuzzy time series model", Computers and Mathematics with Applications 49 539-548, 2005. 12- [Yu, H.-K., 2005] Yu, H.-K., "Weighted fuzzy time series models for TAIEX forecasting", Physica A 349: 609–624, 2005.

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