Neuro-Fuzzy Modelling of Time Series

  • Jianwei Zhang
  • Alois Knoll
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 76)


This paper proposes an approach for the multivariate modelling of time series with neuro-fuzzy systems. The fuzzy rule model is based on adaptive B-splines which can approximate any given input-output data series of low dimension. To efficiently describe high-dimensional input data, statistical indices are extracted to feed the fuzzy controller. The original input space is transformed into an eigenspace. If a sequence of training data are sampled in a local context, a small number of eigenvectors which possess larger eigenvalues provide a good summary of all the original variables. Fuzzy controllers can be trained for mapping the input projection in the eigenspace to the outputs. Experiments of time series prediction validate the concept.


Fuzzy Rule Input Space Fuzzy Controller Linguistic Term Input Selection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. S. Albus. A new approach to manipulator control: The Cerebellar Model Articulation Controller (CMAC). Transactions of ASME, Journal of Dynamic Systems Measurement and Control, 97: 220–227, 1975.CrossRefGoogle Scholar
  2. 2.
    W. Böhm, G. Farin, and J. Kahmann. A survey of curve and surface methods in cagd. Computer Aided Geometric Design, 1: 1–60, 1984.CrossRefGoogle Scholar
  3. 3.
    G. E. P. Box and G. M. Jenkins. Time series analysis. Holden Day, San Francisco, 1970.Google Scholar
  4. 4.
    S. L. Chiu. Selecting input variables for fuzzy models. Journal of Intelligent and Fuzzy Systems, 4: 243–256, 1996.Google Scholar
  5. 5.
    J.-S. R. Jang. ANFIS: Adaptive-network-based fuzzy inference system. IEEE Transactions on System, Man and Cybernetics, 23 (3): 665–685, 1993.CrossRefGoogle Scholar
  6. 6.
    J.-S. R. Jang, C.-T. Sun, and E. Mizutani. Neuro-Fuzzy and Soft Computing. Prentice Hall, 1997.Google Scholar
  7. 7.
    V. Lacrose and A. Tilti. Fusion and hierarchy can help fuzzy logic controller designers. In IEEE International Conference on Fuzzy Systems, Barcelona, 1997.Google Scholar
  8. 8.
    S. Lotvonen, S. Kivikunnas, and E. Juuso. Tuning of a fuzzy system with genetic algorithms and linguistic equations. In Proceedings of Fourth European Congress on Intelligent Techniques and Soft Computing, Aachen, 1997.Google Scholar
  9. 9.
    S. Mitaim and B. Kosko. What is the best shape of a fuzzy set in function approximation. In IEEE International Conference on Fuzzy Systems, pages 1237–1243, 1996.Google Scholar
  10. 10.
    E. Oja. Subspace methods of pattern recognition. Research Studies Press, Hertfordshire, 1983.Google Scholar
  11. 11.
    T. Takagi and M. Sugeno. Fuzzy identification of systems and its application to modelling and control. IEEE Transactions on System, Man and Cybernetics, SMC-15(1): 116–132, 1985.Google Scholar
  12. 12.
    L. A. Zadeh. Fuzzy logic = computing with words. IEEE Trans. on Fuzzy Systems, 4 (2): 103–111, 1996.CrossRefGoogle Scholar
  13. 13.
    J. Zhang and A. Knoll. Constructing fuzzy controllers with B-spline models-principles and applications. International Journal of Intelligent Systems, 13 (2/3): 257–285, 1998.CrossRefGoogle Scholar
  14. 14.
    J. Zhang and A. Knoll. Designing fuzzy controllers by rapid learning Fuzzy Sets and Systems, 13 (2), 1998.Google Scholar
  15. 15.
    J. Zhang, A. Knoll, and I. Renners. Efficient learning of non-uniform B-splines for modelling and control. In International Concerence on Computational Inteligence for Modelling, Control and Automation, Viena, pages 282–287, Viena, 1999.Google Scholar

Copyright information

© Physica-Verlag Heidelberg 2001

Authors and Affiliations

  • Jianwei Zhang
    • 1
  • Alois Knoll
    • 1
  1. 1.Faculty of TechnologyUniversity of BielefeldBielefeldGermany

Personalised recommendations