三层前向神经网络的一致逼近性(英文)  

Uniform Approximation of Three-Layer Feedforward Neural Networks

作　　者：刘普寅[1] 李洪兴[1] 

机构地区：[1]北京师范大学数学系

出　　处：《模糊系统与数学》2003年第2期10-18,共9页Fuzzy Systems and Mathematics

基　　金：National Natural Science Foundation(6 9974 0 4 1;6 0 174 0 13)

摘　　要：近年来 ,前向神经网络泛逼近的一致性分析一直为众多学者所重视。本文系统分析三层前向网络对于拟差值保序函数族的一致逼近性 ,其中 ,转换函数σ是广义 Sigmoidal函数。并将此一致性结果用于建立一类新的模糊神经网络 (FNN) ,即折线 FNN.研究这类网络对于两个给定的模糊函数的逼近性 ,相关结论在分析折线 FNN的泛逼近性时起关键作用。The issue of uniformity analysis for universal approximation of feedforward neural networks has drawn significant attention. In the paper, uniform approximation of three-layer feedforward neural networks to a function family which is called quasi-difference order-preserved set is analyzed, systematically, when the transfer function σ is a generalized Sigmoidal function. Polygonal fuzzy neural network(FNN) is presented. And uniformity result is applied to the construction of a polygonal FNN which can with arbitrary degree of accuracy approximate two special fuzzy functions, which play key roles in approximation of increasing fuzzy functions by the polygonal FNN.

关 键 词：前向神经网络 一致逼近性 拟差值保序函数族 转换函数 广义Sigmoidal函数 模糊神经网络 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]