摘要
积分模是刻画一类可积函数空间的一个度量,分片线性函数是连通模糊系统和被逼近函数关系的桥梁,二者是研究广义模糊系统逼近性问题的两个重要工具.首先通过拓广K-拟算术运算重新定义了Kp-积分模,并依据积分转换定理证明该积分模关于拟加运算构成一个度量.其次,在Kp-积分模意义下获得了分片线性函数可按任意精度逼近一类μp-可积函数.
Integral norm is a metric to describe a class of integrable function space, piecewise linear function is a bridge to connect relationship between fuzzy system and approximation function. They are two important tools to study the approximation problem of generalized fuzzy system. Firstly, the Kp-integral norm is defined by extending the quasi-subtraction operator, and we proved that the Kp-integral norm is a metric about quasi-addition operator by the integral transformation theorem. Secondly, it is obtained that the piecewise linear functions can approximate a kind of μp-integrable functions to arbitrary accuracy with respect to the Kp-integral norm.
出处
《系统科学与数学》
CSCD
北大核心
2016年第2期267-277,共11页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(61374009)资助课题
关键词
K-拟算术运算
μp-可积函数
Kp-积分模
分片线性函数
逼近性.
K-quasi-arithmetic operation,μp-integrable function, Kp-integral norm,piecewise linear function, approximation.
