Neurofuzzy Approximator based on Mamdani’s Model
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.
KeywordsNumerical Data Input Space Linguistic Information Linguistic Rule Crisp Input
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- E.H. Mamdani, “Applications of fuzzy, algorithms for simple dynamic plant”, Proc. IEE, Vol. 121,No. 12,1974,pp. 1585–1588.Google Scholar
- L.X. Wang, Adaptive fuzzy systems and control, Prentice-Hall, Englewood Cliffs, NJ, 1994.Google Scholar
- J.S.R. Jang, C.T. Sun, and E. Mizutani, Neuro-fuzzy and soft computing, Prentice-Hall, NJ, USA, 1997.Google Scholar
- 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
- J.C. Bezdeck, Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York, 1981.Google Scholar
- 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
- M.H. Hassoun, Fundamentals of artificial neural networks, MIT Press, Cambridge, Mass., 1996.Google Scholar
- T. Kohonen, Self-organizing maps, Springer, 1995.Google Scholar
- 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
- 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
- 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
- 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