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$K_p$-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$K_p$-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${\hat{\mu }}_p$-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 ${\hat{\mu }}_p$-integrable functions to arbitrary accuracy with respect to the $Kp$-integral norm.