Skip to main content

Neurofuzzy Approximator based on Mamdani’s Model

  • Conference paper
Neural Nets WIRN Vietri-01

Part of the book series: Perspectives in Neural Computing ((PERSPECT.NEURAL))

Abstract

Neurofuzzy approximators can take on numerous alternatives, as a consequence of the large body of options available for defining their basic operations. In particular, the extraction of the rules from numerical data can be conveniently based on clustering algorithms. The large number of clustering algorithms introduces a further flexibility. Neurofuzzy approximators can treat both numerical and linguistic sources. The analysis of approximator sensitivity to the previous factors is important in order to decide the best solution in actual applications. This task is carried out in the present paper by recurring to illustrative examples and exhaustive simulations. The results of the analysis are used for comparing different learning algorithms. The underlying approach to the determination of the optimal approximator architecture is constructive. This approach is not only very efficient, as suggested by learning theory, but it is also particularly suited to combat the effect of noise that can deteriorate the numerical data.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.H. Mamdani, “Applications of fuzzy, algorithms for simple dynamic plant”, Proc. IEE, Vol. 121,No. 12,1974,pp. 1585–1588.

    Google Scholar 

  2. T. Takagi, and M. Sugeno, “Fuzzy identification of systems and its application to modelling and control”, IEEE Trans. Syst. Man Cybern., Vol. 15, 1985, pp. 116–132.

    MATH  Google Scholar 

  3. J.M. Mendel, “Fuzzy logic systems for engineering: a tutorial”, Proc. IEEE, Vol. 83, No. 3,1995, pp. 345–377.

    Article  Google Scholar 

  4. L.X. Wang, Adaptive fuzzy systems and control, Prentice-Hall, Englewood Cliffs, NJ, 1994.

    Google Scholar 

  5. J.S.R. Jang, C.T. Sun, and E. Mizutani, Neuro-fuzzy and soft computing, Prentice-Hall, NJ, USA, 1997.

    Google Scholar 

  6. G.A. Carpenter, S. Grossberg, et al., “Fuzzy ARTMAP: a neural network architecture for incremental supervised learning and analog multidimensional maps”, IEEE Trans, on Neural Networks, Vol. 3, 1992, pp. 698–713.

    Article  Google Scholar 

  7. Ishibuchi, K. Kwon, and H. Tanaka, “Learning of fuzzy neural networks from fuzzy inputs and fuzzy targets”, Proc. of 5th IFSA World Conference, Vol. I, 1993, pp. 147–150.

    Google Scholar 

  8. C.T. Lin, “A neural fuzzy control system with structure and parameter learning”, Fuzzy Sets Syst., Vol. 70, 1995, pp. 183–212.

    Article  Google Scholar 

  9. I. Rojas, H. Pomares, J. Ortega, and A. Prieto, “Self-organized fuzzy system generation from training examples”, IEEE Trans, on Fuzzy Systems, Vol. 8, No. 1, 2000, pp. 23–36.

    Article  Google Scholar 

  10. Y.Q. Zhang, and A. Kandel, “Compensatory neurofuzzy systems with fast learning algorithms”, IEEE Trans, on Neural Networks, Vol. 9, No. 1, 1998, pp. 83–105.

    Article  MathSciNet  Google Scholar 

  11. J.C. Bezdeck, Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York, 1981.

    Google Scholar 

  12. P.K. Simpson, “Fuzzy min-max neural networks-Part. 2: clustering”, IEEE Trans. on Fuzzy Syst., Vol. 1, No. 1, 1993, pp. 32–45.

    Article  Google Scholar 

  13. F.M. Frattale Mascioli, A. Mancini, A. Rizzi, and G. Martinelli, “Function approximation with noisy training data using FBF neural networks”, Proc. Of NC’98, Vienna, Sept. 1998, pp. 900–906.

    Google Scholar 

  14. V.N. Vapnik, The nature of statistical learning theory, Springer-Verlag, 1995.

    MATH  Google Scholar 

  15. J. Rissanen, ‘Modelling by shortest data description”, Automatica, Vol. 14, 1978, pp. 465–471.

    Article  MATH  Google Scholar 

  16. S. Amari, et al., “Asymptotic statistical theory of overtraining and cross-validation”, IEEE Trans, on Neural Networks, Vol. 8, No. 5,1997, pp. 985–996.

    Article  Google Scholar 

  17. G.C. Mouzouris, and J.M. Mendel, “Nonsingleton fuzzy logic systems: theory and application”, IEEE Trans. on Fuzzy Systems, Vol. 5, No. 1, 1997, pp. 56–71.

    Article  Google Scholar 

  18. M.H. Hassoun, Fundamentals of artificial neural networks, MIT Press, Cambridge, Mass., 1996.

    Google Scholar 

  19. Poggio, and F. Girosi, “Networks for approximation and learning”, Proc. Of IEEE, Vol. 78, Sept. 1990, pp. 1481–1497.

    Article  Google Scholar 

  20. L.X. Wang, and J.M. Mendel, “Fuzzy basis functions, universal approximation and orthogonal least squares learning”, IEEE Trans. on Neural Networks, Vol. 3, No. 5,1992, pp. 807–814.

    Article  Google Scholar 

  21. A. Mancini, F.M. Frattale Mascioli, A. Rizzi, and G. Martinelli, “Improving FBF neurofuzzy approximator by optimised input space covering”, Electronics Letters, Vol. 35, No. 4, 18 Feb. 1999, pp. 312–313.

    Article  Google Scholar 

  22. T. Kohonen, Self-organizing maps, Springer, 1995.

    Google Scholar 

  23. T. Kohonen, E. Oja, O. Simula, A. Visa, and J. Kangas, “Engineering applications of the self-organizing maps”, Proc. of IEEE; October 1996, pp. 1358–1384.

    Google Scholar 

  24. F.M. Frattale Mascioli, A. Rizzi, G. Scrocca, and G. Martinelli, “Scale-based clustering via gravitational law imitation”, WIRN-99, Springer, 1999, pp. 256–265.

    Google Scholar 

  25. F.M. Frattale Mascioli, A. Rizzi, and G. Martinelli, “Compactness-separability optimization of fuzzy clusters”, Proc. of ISIS’97, Reggio Calabria, Italy, Sept. 1997, pp. 452–457.

    Google Scholar 

  26. F.M. Frattale Mascioli, A. Rizzi, M. Panella, and G. Martinelli, “Clustering with uncostrained hyperboxes”, IEEE Int. Fuzzy Systems Conference, Seoul, Korea, August 1999, Vol. II, pp. 1075–1080.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag London Limited

About this paper

Cite this paper

Frattale, F.M.M., Mancini, A., Rizzi, A., Panella, M., Martinelli, G. (2002). Neurofuzzy Approximator based on Mamdani’s Model. In: Tagliaferri, R., Marinaro, M. (eds) Neural Nets WIRN Vietri-01. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-0219-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0219-9_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-505-2

  • Online ISBN: 978-1-4471-0219-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics