Abstract
Fuzzy inference systems represent an important part of fuzzy logic. In most practical applications (i.e., control) such systems perform crisp nonlinear mapping, which is specified in the form of fuzzy rules encoding expert or common-sense knowledge about the problem at hand. This paper shows an equivalence between fuzzy system representation and more traditional (mathematical) forms of function parameterization commonly used in statistics and neural nets. This connection between fuzzy and mathematical representations of a function is crucial for understanding advantages and limitations of fuzzy inference systems. In particular, the main advantages are interpretation capability and the ease of encoding a priori knowledge, whereas the main limitation is the lack of learning capabilities. Finally, we outline several major approaches for learning (estimation) of fuzzy rules from the training data.
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References
Brown, M. and C. Harris, Neurofuzzy Adaptive Modeling and Control, Prentice Hall, Englewood Cliffs, N.J. 1994
Cherkassky, V. and H. Lari-Najafi, Data representation for diagnostic neural networks, IEEE Expert, v.7, no.5, 43–53, 1992
Cherkassky, V. and F. Mulier, Learning From Data: Statistical, Neural Network and Fuzzy Modeling, Wiley, 1997 (to appear)
Cherkassky, V., F. Mulier and V. Vapnik, Comparison of VC method with classical methods for model selection, Proc. World Congress on Neural Networks, 957–962, Lawrence Erlbaum, NJ, 1996
Friedman, J.H., An Overview of predictive learning and function approximation, in Cherkassky, Friedman and Wechsler (Eds.), From Statistics to Neural Networks. Theory and Pattern Recognition Applications. Springer, NATO ASI Series, v. 136, 1994
Kosko, B., Neural Networks and Fuzzy Systems: A Dynamical Approach to Machine Intelligence, Prentice Hall, Englewood Cliffs, N.J. 1992
Moody, J.E., Note on generalization,regularization and feature selection in nonlinear learning systems, First IEEE Workshop on Neural Networks in Signal Processing, 1–10, IEEE Comp. Society Press, Los Alamitos, CA, 1991
Vapnik, V.N., The Nature of Statistical Learning Theory, Springer Verlag, 1995
Watkins, F., Fuzzy function representation: the trouble with triangles, Proc. World Congress on Neural Networks, 1123–1126, Lawrence Erlbaum, NJ,1996
Zadeh, L.A., Fuzzy sets, Information and Control, v. 8, 338–353, 1965
Zadeh, L.A., Fuzzy Logic: a precis, Multivalued Logic, v.1, 1–38, Gordon and Breach Science Publishers, 1996
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© 1998 Springer-Verlag Berlin Heidelberg
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Cherkassky, V. (1998). Fuzzy Inference Systems: A Critical Review. In: Kaynak, O., Zadeh, L.A., Türkşen, B., Rudas, I.J. (eds) Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications. NATO ASI Series, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58930-0_10
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DOI: https://doi.org/10.1007/978-3-642-58930-0_10
Publisher Name: Springer, Berlin, Heidelberg
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