前向正则模糊神经网络依K-积分模的泛逼近能力  

Capability of Universal Approximation of Feedforward Regular Fuzzy Neural Networks in K-Integral Norm

作　　者：王贵君[1] 李丹[2] 

机构地区：[1]天津师范大学数学科学学院,天津300387 [2]东北财经大学津桥商学院基础部,大连116622

出　　处：《应用数学学报》2013年第1期141-152,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(60974144)资助项目

摘　　要：针对前向正则模糊神经网络引进K-拟可加积分和K-积分模概念,应用积分转换定理研究了该网络在K-积分模意义下对模糊值简单函数类的泛逼近能力,进而在有限K-拟可加测度空间上,借助模糊值简单函数为桥梁获得了前向正则模糊神经网络依K-积分模对(?)-可积有界模糊值函数类仍具有泛逼近性.该结果表明前向正则模糊神经网络对连续模糊系统的逼近能力可以推广为对一般可积系统的逼近能力.Aim at feedforward regular fuzzy neural networks, the concepts of K-quasi- additive integrals and K-integral norms are introduced. The capability of universal approximation of this network for the class of fuzzy valued simple functions in the sense of K-integral norms is studied by applying integrals transformation theorem. Furthermore, on a finite K-quasi-additive measure space, it is obtained that feedforward regular fuzzy neural networks possess universal approximation for the class of ^u-integrally bounded fuzzy valued functions in K-integral norms by means of fuzzy valued simple functions. This result indicates that the approximation capability which feedforward regular fuzzy neural networks possess for continuous fuzzy systems can be extended as for general integrable systems.

关 键 词：泛逼近性 诱导算子 K-积分模 u-可积有界 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]