Fuzzy Metric Approach for Fuzzy Time Series Forecasting based on Frequency Density Based Partitioning

Authors: Tahseen Ahmed Jilani, Syed Muhammad Aqil Burney, C. Ardil

Abstract:

In the last 15 years, a number of methods have been proposed for forecasting based on fuzzy time series. Most of the fuzzy time series methods are presented for forecasting of enrollments at the University of Alabama. However, the forecasting accuracy rates of the existing methods are not good enough. In this paper, we compared our proposed new method of fuzzy time series forecasting with existing methods. Our method is based on frequency density based partitioning of the historical enrollment data. The proposed method belongs to the kth order and time-variant methods. The proposed method can get the best forecasting accuracy rate for forecasting enrollments than the existing methods.

Keywords: Fuzzy logical groups, fuzzified enrollments, fuzzysets, fuzzy time series.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077541

References:

[1] Chen S. M. and Hsu C.-C. 2004. A new method to forecasting enrollments using fuzzy time series, International Journal of Applied Science and Engineering, 2, 3: 234-244.
[2] Chen, S. M. 1996. Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81: 311-319.
[3] S. M. Chen, J. R. Hwang, "Temperature prediction using fuzzy time series", IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 30, pp.263-275, 2000.
[4] S. M. Chen, "Forecasting enrollments based on high-order fuzzy time series", Cybernetics and Systems: An International Journal, Vol. 33: pp. 1-16, 2002.
[5] K. Huarng, "Heuristic models of fuzzy time series for forecasting", Fuzzy Sets and Systems, Vol. 123, pp. 369-386, 2002.
[6] K. Huarng, "Effective lengths of intervals to improve forecasting in fuzzy time series", Fuzzy Sets and Systems, Vol. 12, pp. 387-394, 2001.
[7] C. C. Hsu, S. M. Chen, "A new method for forecasting enrollments based on fuzzy time series", Proceedings of the Seventh Conference on Artificial Intelligence and Applications, Taichung, Taiwan, Republic of China, pp. 17-22.
[8] J. R. Hwang, S. M. Chen, C. H. Lee, "Handling forecasting problems using fuzzy time series", Fuzzy Sets and Systems, Vol. 100, pp. 217-228, 1998.
[9] T. A. Jilani, S. M. A. Burney, "M-factor high order fuzzy time series forecasting for road accident data", In IEEE-IFSA 2007, World Congress, Cancun, Mexico, June 18-21, Forthcoming in Book series Advances in Soft Computing, Springer-Verlag, 2007.
[10] T. A. Jilani, S. M. A. Burney, C. Ardil, "Multivariate high order fuzzy time series forecasting for car road accidents", International Journal of Computational Intelligence, Vol. 4, No. 1, pp.15-20., 2007.
[11] G. J. Klir, T. A. Folger, Fuzzy Sets, Uncertainty, and Information, Prentice-Hall, New Jersey, U.S.A, 1988.
[12] G. J. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, New Jersey, U.S.A, 2005.
[13] L. W. Lee, L. W. Wang, S. M. Chen, "Handling forecasting problems based on two-factors high-order time series", IEEE Transactions on Fuzzy Systems, Vol. 14, No. 3, pp.468-477, 2006.
[14] H. Li, R. Kozma, "A dynamic neural network method for time series prediction using the KIII model", Proceedings of the 2003 International Joint Conference on Neural Networks, 1: 347-352, 2003.
[15] S. Melike, Y. D. Konstsntin, "Forecasting enrollment model based on first-order fuzzy time series", in proc. International Conference on Computational Intelligence, Istanbul, Turkey, 2004.
[16] Q. Song, "A note on fuzzy time series model selection with sample autocorrelation functions", Cybernetics and Systems: An International Journal, Vol. 34, pp. 93-107, 2003.
[17] Q. Song, B. S. Chissom, "Fuzzy time series and its models", Fuzzy Sets and Systems, Vol. 54, pp. 269-277, 1993.
[18] Q. Song, B. S. Chissom, "Forecasting enrollments with fuzzy time series Part I", Fuzzy Sets and Systems, 54: 1-9.
[19] Q. Song, B. S. Chissom, "Forecasting enrollments with fuzzy time series: Part II", Fuzzy Sets and Systems, Vol. 62: pp. 1-8, 1994.
[20] Q. Song, R. P. Leland, "Adaptive learning defuzzification techniques and applications", Fuzzy Sets and Systems, Vol. 81, pp. 321-329, 1996.
[21] S. F. Su, S. H. Li," Neural network based fusion of global and local information in predicting time series", Proceedings of the 2003 IEEE International Joint Conference on Systems, Man and Cybernetics, No. 5: pp. 4445-4450, 2003.
[22] J. Sullivan, W. H. Woodall, "A comparison of fuzzy forecasting and Markov modeling", Fuzzy Sets and Systems, Vol. 64, pp.279-293, 1994.
[23] L. X. Wang, J. M. Mendel, "Generating fuzzy rules by learning from examples", IEEE Transactions on Systems, Man, and Cybernetics, Vol. 22, pp.1414-1427, 1992.
[24] H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer Publishers, Boston, USA. 2001.