三层前向神经网络的一致逼近性(英文)

Uniform Approximation of Three-Layer Feedforward Neural Networks

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.