Construction and Design of Parsimonious Neurofuzzy Systems

  • K. M. Bossley
  • D. J. Mills
  • M. Brown
  • C. J. Harris
Part of the Advances in Industrial Control book series (AIC)


Static fuzzy systems have been extensively applied in the Far East to a wide range of consumer products whereas researchers in the west have mainly been concerned with developing adaptive neural network that can learn to perform ill-defined, difficult tasks. Neurofuzzy systems attempt to combine the best aspects of each of these techniques as the transparent representation of a fuzzy system is fused with the adaptive capabilities of a neural network, while minimising the undesirable features. As such, they are applicable to a wide range of static, design problems and on-line adaptive modelling and control applications. This chapter focuses on how an appropriate structure for the rule base may be determined directly from a set of training data. It provides the designer with valuable qualitative information about the physics of the underlying process as well as improving the network’s generalisation abilities and the condition of the learning problem.


Partial Little Square Fuzzy Rule Input Space Multivariate Adaptive Regression Spline Quad Tree 
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.


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  1. 1.
    Barron, A.R. Universal approximation bounds for superposition of a sigmoidal function. IEEE Trans. on Information Theory, 39(3):930–945, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bellman R.E. Adaptive Control Processes. Princeton University Press, 1961.zbMATHGoogle Scholar
  3. 3.
    Brown M. and Harris C.J. Neurofuzzy Adaptive Modelling and Control. Prentice Hall, Hemel Hempstead, 1994.Google Scholar
  4. 4.
    Buja A., Hastie T. and Tibshirani R. Linear smoothers and additive models. The Annuals of Statistics, 17(2):453–535, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Farlow S.J. The GMDH algorithm. In Self-Organising Methods in Modelling, pages 1–24. Marcel Decker, Statisticsitextbooks and monographs vol. 54, 1984.Google Scholar
  6. 6.
    Fraser R.J.C. Embedded command and control infrastructures for intelligent autonomous systems. PhD thesis, Department of Aeronautics and Astronautics, University of Southampton, U.K., 1994.Google Scholar
  7. 7.
    Friedman J.H. Multivariate Adaptive Regression Splines. The Annals of Statistics, 19(1):1–141, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Friedman J.H. and Stuetzle W. Projection pursuit regression. Journal of the American Statistical Association, 76(376):817–823, 1981.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gnanadesikan R. Methods for Statistical Data Analysis of Multivariate Observations. John Wiley And Sons, New York, 1977.zbMATHGoogle Scholar
  10. 10.
    Hastie T.J. and Tibshirani R.J. Generalized Additive Models. Chapman and Hall, 1990.zbMATHGoogle Scholar
  11. 11.
    Hwang J., Lay S., Maechler M., Douglas R. and Schimet J. Regression model in back-propagation and projection pursuit learning. IEEE Transactions on neural networks, 5(3), 1994.Google Scholar
  12. 12.
    Kavli T. Learning Principles in Dynamic Control. PhD thesis, University of Oslo, Norway, 1992.Google Scholar
  13. 13.
    Kavli T. ASMOD: an algorithm for Adaptive Spline Modelling of Observation Data. International Journal of Control, 58(4):947–968, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Lane S., Flax M.G., Handelman D.A. and Gelfand J. Multi-layered perceptrons with b-spline receptive field functions. NIPS, 3:684–692, 1991.Google Scholar
  15. 15.
    Lines G.T. Nonlinear Empirical Modelling Using Projection Methods. PhD thesis, Department of informatics, University of Oslo, 1994.Google Scholar
  16. 16.
    Ljung L. System Identification: Theory for the User. Information and System Sciences Series. Prentice Hall, Englewood Cliffs, NJ, 1987.zbMATHGoogle Scholar
  17. 17.
    Moody J. Fast learning in multi-resolution hierarchies. In Advances in Neural Information Processing Systems I, pages 29–39. Morgan Kaufmann, 1989.Google Scholar
  18. 18.
    Murray-Smith R. A local model network approach to nonlinear modelling. PhD thesis, Department of Computer Science, University of Strathclyde, 1994.Google Scholar
  19. 19.
    Nakamori Y. and Ryoke M. Identification of fuzzy prediction models through hyperellisoidal clustering. IEEE Transactions on systems, man, and cybernetics, 24(8):1153–1173, 1994.CrossRefGoogle Scholar
  20. 20.
    Peel C., Willis M.J. and Tham M.T. A fast procedure for the training of neural networks. Journal of Process Control, 2(4):205–211, 1992.CrossRefGoogle Scholar
  21. 21.
    Poggio T. and Girosi F. Neural networks for approximation and learning. Proceedings of the IEEE, 78(9):1481–1497, 1990.CrossRefGoogle Scholar
  22. 22.
    Roberts J.M. and Mills D.J. and Charnley D. and Harris C.J. Improved kalman filter initialisation using neurofuzzy estimation, submited to: 4th IEE International Conference on Artificial Neural Networks, 1994.Google Scholar
  23. 23.
    Rumbaugh J., Blaha M., Premerlani W., Eddy F. and Lorensen W. Object-oriented Modeling and Design. Prentice Hall, Englewood Cliffs, New Jersey, 1991.Google Scholar
  24. 24.
    Sanger T.D. Neural network learning control of robot manipulators using gradually increasing task difficulty. IEEE Trans. on Robotics and Automation, 10(3):323–333, 1994.CrossRefGoogle Scholar
  25. 25.
    Shewchuk J.R. An introduction to the conjugate gradients method without the agonizing pain. Technical Report CMU-CS-94–125, School of Computer Science, Carnegie Mellon University, 1994.Google Scholar
  26. 26.
    Sugeno, M. and Kang, G.T. Structureed identification of fuzzy model. Fuzzy Sets and Systems, North-Holland, 28:15–33, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Sun C. Rule-base structure identification in a adaptive network based inference system. IEEE Transactions on Fuzzy Systems, 2(1), 1994.Google Scholar
  28. 28.
    Wedd A.R. An approach to nonlinear princple component analysis using radial basis functions. Technical Report memo 4739, Defence Research Agency Malvern, 1993.Google Scholar
  29. 29.
    Werntges H.W. Partitions of unity improve neural function approximation. IEE International Conference on Neural Networks, 2:914–918, 1993.CrossRefGoogle Scholar
  30. 30.
    Wold S. Nonlinear partial least squares modelling. II spline inner relation. Chemo-metrics and Intelligent Laboratory Systems, 14:71–94, 1992.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1995

Authors and Affiliations

  • K. M. Bossley
    • 1
  • D. J. Mills
    • 1
  • M. Brown
    • 1
  • C. J. Harris
    • 1
  1. 1.Image, Speech and Intelligent Systems Research Group Department of Electronics and Computer ScienceUniversity of SouthamptonUK

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