K-积分模意义下折线模糊神经网络的泛逼近性

为克服模糊数运算的复杂性引入折线模糊数的定义,利用折线模糊数的优良性质获得了两个重要不等式,并给出实例说明折线模糊数的逼近能力有效.其次,引进K-拟可加积分和K-积分模概念,在折线模糊数空间满足可分性的基础上,借助于模糊值简单函数和模糊值Bernstein多项式研究了若干函数空间的稠密性问题,获得了可积有界模糊值函数类依K-积分模构成完备可分的度量空间.最后,在K-积分模意义下讨论了四层正则折线模糊神经网络对模糊值简单函数的泛逼近性,进而得到该网络对可积有界函数类也具有泛逼近性.该结果表明正则折线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.

Universal approximation of polygonal fuzzy neural networks in sense of K-integral norms

In this paper,we introduce polygonal fuzzy numbers to overcome the operational complexity of ordinary fuzzy numbers,and obtain two important inequalities by taking advantage of their fine properties.By presenting an actual example,we demonstrate that the approximation capability of polygonal fuzzy numbers is efficient.Furthermore,the concepts of K-quasi-additive integrals and K-integral norms are introduced.Whenever the polygonal fuzzy numbers space satisfies separability,the density problems for several functions spaces can be studied,by means of fuzzy-valued simple functions and fuzzy-valued Bernstein polynomials.We establish that the class of the integrally-bounded fuzzy-valued functions spans a complete and separable metric space in the K-integral norms.Finally,in the sense of K-integral norms,the universal approximation of four-layer regular polygonal fuzzy neural networks for fuzzy-valued simple functions is discussed.Furthermore,we show that this type of networks also possesses universal approximation for the class of integrally-bounded fuzzy-valued functions.This result indicates that the approximation capability which regular polygonal fuzzy neural networks for continuous fuzzy systems can be extended as for general integrable systems.