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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 multidimensional piecewise linear function is a generalized extension of a piecewise piecewise linear function in multivariate cases and plays an important role as a bridge in the study of the approximation of fuzzy systems. Aiming at a class of u-integrable functions, And the definition of space and hyperplane construct a multidimensional piecewise linear function, and then prove that the piecewise linear function has approximation performance for a given u-integrable function according to the K-integral modulus. The results show that in the fuzzy system, The approximation ability of linear function to continuous function can be generalized to the approximation ability of general integrable function.