Abstract
Although many works have been done in recent years for the designing Fuzzy-Neural Networks (FNN) from input-output data, the results concerning how to analyze the performance of some methods from a rigorous mathematical point of view are somewhat few. In this paper, the approximation bound for the Table Look-up Scheme with the Bell Membership Function is established. The detailed formulas of the error bound between the nonlinear function to be approximated and the FNN system designed based on the input-output data are derived.
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References
Wang, L.X., Mendel, J.M.: Fuzzy Basis Functions, Universal Approximation, and orthogonal least squares learning. IEEE Trans. Neural Network. 3, 807–814 (1992)
Wang, L.X.: Generating Fuzzy Rules by Learning from Examples. IEEE Trans Syst., Man, Cybern. 22, 1414–1427 (1992)
Wang, L.X., Chen, W.: Approximation Accuracy of Some Neuro-Fuzzy Approches. IEEE Trans. Fuzzy Systems 8, 470–478 (2000)
Chen, T.P., Chen, H.: Approximation Capability to Functions of Several Variables, Nonlinear Functions, and Operators by Radial Function Neural Networks. IEEE Trans. Neural Networks 6, 904–910 (1995)
Maiorov, V., Meir, R.S.: Approximation Bounds for Smooth Functions in C(R d) by Neural and Mixture Networks. IEEE Trans. Neural Networks 9, 969–978 (1998)
Burger, M., Neubauer, A.: Error Bounds for Approximation with Neurnal Networks. J. Approx. Theory 112, 235–250 (2001)
Ma, W.M., Chen, G.Q.: Improvement on the Approximation Bound for Fuzzy-Neural Networks Clustering Method with Gaussian Membership Function. In: Li, X., Wang, S., Dong, Z.Y. (eds.) ADMA 2005. LNCS (LNAI), vol. 3584, pp. 225–231. Springer, Heidelberg (2005)
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Ma, W. (2006). Approximation Accuracy of Table Look-Up Scheme for Fuzzy-Neural Networks with Bell Membership Function. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893295_112
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DOI: https://doi.org/10.1007/11893295_112
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46484-6
Online ISBN: 978-3-540-46485-3
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