The paper presents novel modeling of fuzzy inference system by using the ‘fuzzified’ radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calculus with fuzzy numbers. Prior the mapping, both the antecedents and the consequents are discretized and transferred into the n-dimensional and m-dimensional ‘fuzzy’ vectors. These vectors present the training inputs and outputs of an RBF NN and, in this way, an RBF network performs an exact R n → R m mapping. The generalization capacity of such a neural implementation is superior to the ability of the original fuzzy model.
- Membership Function
- Radial Basis Function
- Fuzzy Number
- Fuzzy Model
- Inference Rule
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.
This is a preview of subscription content, access via your institution.
Unable to display preview. Download preview PDF.
Hayashi, Y., J.J Buckley and E. Czogala. Fuzzy neural network with fuzzy signals and weights. Internat. J. Intelligent Systems 8, pp., 527–537, 1993.
Ishibuchi, H., R. Fujioka and H. Tanaka. Neural networks that learn from fuzzy if-then rules. IEEE Trans. Fuzzy system 1(2), pp., 85–97, 1993a.
Ishibuchi, H. Okada and H. Tanaka. Fuzzy neural networks with fuzzy weights and fuzzy biases. Proc. ICNN’93, San Francisco pp., 1650–1655, 1993b.
Ishibuchi, H. Okada and H. Tanaka. Interpolatin of fuzzy if-then rules by neural net works. International Journal of Approximate Reasoning 10 (1), pp., 3–27, 1994.
Ishibuchi, H., K. Kwon and H. Tanaka. A learning algorithm of fuzzy neural networks with triangular fuzzy weights. Fuzzy Sets and Systems 71, pp., 277–293, 1995a.
Ishibuchi, H., K. Morioka and I.B. Turksen. Learning by fuzzified neural net works. International Journal of Approximate Reasoning 13, pp., 327–358, 1995b.
Jang, J.-S.R., Sun, T.-C., ‘Functional equivalence between radial basis function net works and fuzzy inference systems’, IEEE Trans. on NN, 4(1), pp. 156–159, 1993
Kecman V., Pfeiffer B-M., ‘Exploiting the Structural Equivalence of Learning Fuzzy Systems and Radial Basis Function Neural Networks’, 2-nd Europ. Congr. on Intell. Techn. and Soft Comput., EUFIT ‘84, Aachen, Vol. 1, pp. 58–66, 1994.
Kecman, V. V., ‘Learning and Soft Computing, Support Vector Machines, Neural Networks, and Fuzzy Logic Models’, The MIT Press, Cambridge, MA, USA, 2001.
Li, Z.Q., Kecman, V., Ichikawa, A., ‘Fuzzified Neural Network Based on Fuzzy Number Operations’, Fuzzy Sets and Systems, (to appear), 2002.
Editors and Affiliations
Rights and permissions
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kecman, V., Li, Z. (2003). Fuzzy Calculus by RBF Neural Networks. In: Rutkowski, L., Kacprzyk, J. (eds) Neural Networks and Soft Computing. Advances in Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1902-1_79
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0005-0
Online ISBN: 978-3-7908-1902-1
eBook Packages: Springer Book Archive