Zhu Xiaoming, Wang Shitong. Universal approximation of hierarchical fuzzy systems and their relationship with multiwavelet neural networks[J]. Journal of Electronics & Information Technology, 2002, 24(7): 921-928.
Citation:
Zhu Xiaoming, Wang Shitong. Universal approximation of hierarchical fuzzy systems and their relationship with multiwavelet neural networks[J]. Journal of Electronics & Information Technology, 2002, 24(7): 921-928.
Zhu Xiaoming, Wang Shitong. Universal approximation of hierarchical fuzzy systems and their relationship with multiwavelet neural networks[J]. Journal of Electronics & Information Technology, 2002, 24(7): 921-928.
Citation:
Zhu Xiaoming, Wang Shitong. Universal approximation of hierarchical fuzzy systems and their relationship with multiwavelet neural networks[J]. Journal of Electronics & Information Technology, 2002, 24(7): 921-928.
In this paper, the characteristics of B-spline basis functions are first introduced, and the universal approximation properties of hierarchical fuzzy systems based on B-spline basis functions are verified, and then, another new proof on approximation property of multiwavelet neural network is given using the equivalence relation between B-spline-basis-function-based fuzzy system(HBFS) and wavelet neural network. All of these provide solid theoretical foundation for HBFS s application.
Wang Lixin, Universal approximation by hierarchical fuzzy systems, Fuzzy Sets and Systems.1998. 93(2), 142-148.[2]潘进,焦李成,多子波神经网络及其逼近性,电子学报,2000,28(10),60-64[3]M.J..D.Power, Approximation Theory and Methods, Cambridge, Cambridge University Press.1981, Chapter 4. ［4］於东军,王士同,B样条神经网络的构造理论,计算机研究与发展,1999,36(5),534-540[4]Yi Yu, Shaohua Tan, Complementarity and equivalence relationships between convex fuzzy systems with symmetry restrictions and wavelets, Fuzzy Sets and Systems, 1999, 101(3), 423-438.
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