一般输入的折线模糊神经网络对模糊函数的通用逼近

Universal Approximation of Fuzzy Functions by Polygonal Fuzzy Neural Networks with General Inputs

首先基于一种扩展原理和模糊算术得到一类前向模糊神经网络——折线模糊神经网络.当模糊神经网络的输入为一般模糊数,激励函数为单调连续型Sigmoidal函数时,分析网络的拓扑结构及相关性质.然后证明该折线模糊神经网络能作为模糊连续函数的通用逼近器,其等价条件是模糊函数的递增性.因此关于输入为一般模糊数的折线模糊网络是否为通用逼近器的问题得到解决,且折线模糊神经网络的应用范围将进一步扩大.

Firstly, a class of feedforward fuzzy neural networks （FNNs） , polygonal FNNs, is proposed based on a redefined extension principle and fuzzy arithmetic. Then, while the inputs are general fuzzy numbers and the active functions are monotone continuous sigmoid functions, the topologic structure and the related properties of the polygonal FNNs are analyzed systemically. Some theorems for the continuous fuzzy function can be approximated to any degree of accuracy by polygonal FNN and they are proved. Finally, the equivalent conditions are presented. Thus the problem whether the polygonal FNNs with general inputting fuzzy numbers is the universal approximator to the class of continuously increasing fuzzy function is solved, and consequently the application areas of polygonal fuzzy neural networks are extended.