多维分片线性函数是一元分段线性函数在多元情况下的推广, 它在研究模糊系统的逼近性中起到重要的桥梁作用. 文章针对一类~{\it \^{u}}-可积函数, 通过剖分模糊系统输入空间和超平面的定义构造了一个多维分片线性函数, 进而证明了 该分片线性函数依$K$-积分模为度量对给定  ~{\it \^{u}}-可积函数具有逼近性能.结果表明, 模糊系统中分片线性函数对连续函数的逼近能力可以推广为对一般可积函数的逼近能力.

The multi-dimensional piecewise linear function is a generalization of  a variable subsection linear function in the case of multiple variables,  which plays an important bridge role in the approximation research of fuzzy systems. In this paper, for a class of ~{\it \^{u}}-integrable functions, we divide the input space of a
fuzzy system in order to construct a multi-dimensional piecewise linear function by the definition of an hyperplane, and then, we prove that the piecewise linear function have the approximation performance according to the $K$-integral model metric for a {\it \^{u}}-integrable function. The results show that the approximation ability of the piecewise linear functions for a continuous function can be extended to general integrable function in fuzzy systems.