层次模糊系统的全局逼近性质及其与多子波神经网络关系研究
Universal approximation of hierarchical fuzzy systems and their relationship with multiwavelet neural networks
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摘要: 该文首先讨论了B样条基函数的特性,在此基础上证明了基于B样条隶属函数的层次模糊系统(HBFS)是全局逼近器这一重要结论。与此同时,根据基于B样条隶属函数的层次模糊系统与多子波神经网络在逼近问题上的等价性,我们对于多子波神经网络是否为全局逼近器这一问题给出了一种全新的证明方法,以上工作为HBFS的实际应用提供了坚实的的理论基础。Abstract: 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.
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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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