×

Applications of type-2 fuzzy logic systems to forecasting of time-series. (English) Zbl 1060.62554

Summary: We begin with a type-1 fuzzy logic system (FLS), trained with noisy data. We then demonstrate how information about the noise in the training data can be incorporated into a type-2 FLS, which can be used to obtain bounds within which the true (noisefree) output is likely to lie. We do this with the example of a one-step predictor for the Mackey-Glass chaotic time-series [M.C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197, 287–289 (1977)]. We also demonstrate how a type-2 FLS can be used to obtain better predictions than those obtained with a type-1 FLS.

MSC:

62M20 Inference from stochastic processes and prediction
37M10 Time series analysis of dynamical systems
03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, second ed., Springer, New York, 1991; P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, second ed., Springer, New York, 1991 · Zbl 0709.62080
[2] Cichocki, A.; Unbehauen, R., Neural Networks for Optimization and Signal Processing (1994), Wiley & Teubner: Wiley & Teubner Stuttgasrt
[3] J.R. Deller Jr., M. Nayeri, S. Odeh, Least-square identification with error bounds for real-time signal-processing and control, in: Proceedings of the IEEE, June 1993, vol. 81, no. 6; J.R. Deller Jr., M. Nayeri, S. Odeh, Least-square identification with error bounds for real-time signal-processing and control, in: Proceedings of the IEEE, June 1993, vol. 81, no. 6
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[5] N.N. Karnik, J.M. Mendel, An Introduction to type-2 fuzzy logic systems, October 1998, USC Report. http://sipi.usc.edu/∼mendel/report; N.N. Karnik, J.M. Mendel, An Introduction to type-2 fuzzy logic systems, October 1998, USC Report. http://sipi.usc.edu/∼mendel/report
[6] N.N. Karnik and J.M. Mendel, Introduction to Type-2 Fuzzy Logic Systems, Proc. 1998 IEEE FUZZ Conference, Anchorage, AK, May, pp. 915-920; N.N. Karnik and J.M. Mendel, Introduction to Type-2 Fuzzy Logic Systems, Proc. 1998 IEEE FUZZ Conference, Anchorage, AK, May, pp. 915-920
[7] N.N. Karnik, J.M. Mendel, Operations on type-2 fuzzy sets, Fuzzy Sets and Systems, submitted; N.N. Karnik, J.M. Mendel, Operations on type-2 fuzzy sets, Fuzzy Sets and Systems, submitted · Zbl 1010.03047
[8] N.N. Karnik, J.M. Mendel, Applications of type-2 fuzzy logic systems: handling the uncertainty associated with surveys, Proc. FUZZ-IEEE ’99. Seoul, Korea, August 1999, pp. 1546-1551; N.N. Karnik, J.M. Mendel, Applications of type-2 fuzzy logic systems: handling the uncertainty associated with surveys, Proc. FUZZ-IEEE ’99. Seoul, Korea, August 1999, pp. 1546-1551
[9] N.N. Karnik, J.M. Mendel, Type-2 Fuzzy Logic Systems: Type-Reduction, Proc. 1998 IEEE SMC Conference, San Diego, CA, October 1998; N.N. Karnik, J.M. Mendel, Type-2 Fuzzy Logic Systems: Type-Reduction, Proc. 1998 IEEE SMC Conference, San Diego, CA, October 1998
[10] Karnik, N. N.; Mendel, J. M.; Liang, Q., Type-2 fuzzy logic systems, IEEE Transactions on Fuzzy Systems, 7, 5 (1999)
[11] Kaufmann, A.; Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications (1991), Van Nostrand Reinhold: Van Nostrand Reinhold New York · Zbl 0754.26012
[12] Kim, D.; Kim, C., Forecasting time series with genetic fuzzy predictor ensemble, IEEE Transactions on Fuzzy Systems, 5, 1, 523-535 (1997)
[13] Mackey, M. C.; Glass, L., Oscillation and chaos in physiological control systems, Science, 197, 287-289 (1977) · Zbl 1383.92036
[14] Mizumoto, M.; Tanaka, K., Some properties of fuzzy sets of type-2, Information and Control, 31, 312-340 (1976) · Zbl 0331.02042
[15] Mouzouris, G. C.; Mendel, J. M., Nonsingleton fuzzy logic systems: theory and application, IEEE Transactions on Fuzzy Systems, 5, 1, 56-71 (1997)
[16] Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11, 5, 341-356 (1982) · Zbl 0501.68053
[17] Pawlak, Z., Rough classification, International Journal of Man-Machine Studies, 20, 469-483 (1984) · Zbl 0541.68077
[18] Walter, E.; Piet-Lahanier, H., Estimation of parameter bounds from bounded-error data: a survey, Mathematics and Computers in Simulation, 32, 449-468 (1990)
[19] Wang, L.-X.; Mendel, J. M., Generating fuzzy rules by learning from examples, IEEE Transactions on Systems, Man and Cybernetics, 22, 60, 1414-1427 (1992)
[20] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning-1, Information Sciences, 8, 199-249 (1975) · Zbl 0397.68071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.