以四边形隶属函数作为一般的隶属函数，利用Stone-Weierstrass定理对任意隶属函数的模糊系统任意逼近紧集上的任意连续实函数进行证明，是对基本模糊系统逼近任意连续非线性函数理论的推广，模糊系统对任意非线性函数的逼近性能，是模糊系统用于系统辩识的理论依据。

While quadrilateral membership function is used as general membership function, Stone-Weierstrass theorem is utilized to prove that fuzzy systems with arbitrary membership functions are capable of approximating any continuous function on a compact set. It is a generalization for theory of basic fuzzy systems approximating any continuous non-linear function. The performance of fuzzy systems to approximate random non-linear function is the theoretical basis of fuzzy system's application in system identification.