Universal Approximation of Fuzzy Functions by Polygonal Fuzzy Neural Networks with General Inputs
He Chun · 2009
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.