【摘要】 分片线性函数是一元分段线性函数在多元情况下的推广,它在沟通模糊系统和被逼近函数关系中起着重要的桥梁作用.文章基于多元连续函数的网格分片线性函数(grid piecewise linear function,GPLF)重新构造了非齐次线性T-S模糊系统,并依据行列式性质和矩阵模证明了当规则后件线性部分所有参数选取非零常数时该系统对GPLF也具有逼近性.进而在最大模意义下获得该线性T-S模糊系统对连续函数类构成逼近器.此外,通过模拟实例对非齐次线性T-S模糊系统进行逼近精度分析.结果显示,该非齐次线性T-S模糊系统可按任意精度逼近所给连续函数.更多还原

【Abstract】 The piecewise linear function is a generalization for an variable segmented linear function in multivariate case,which plays an important role as a bridge to communicate fuzzy systems and approximated functions.In this paper,we reconstruct the nonhomogeneous linear T-S fuzzy systems based on the grid piecewise linear functions(GPLF) of a multivariate continuous function,and according to the properties of the determinant and matrix norm,we also prove that this system can approximate the GPLF whenever all parameters of a linear part in the consequents of the rules take nonzero constants.And then,it is obtained that the linear T-S fuzzy system constitutes an approximator to continuous function class in the sense of the maximum norm.In addition,through a simulation example,the approximation accuracy of nonhomogeneous linear T-S fuzzy systems is analyzed.The results show that the nonhomogeneous linear T-S fuzzy system can approximate the given continuous functions to arbitrary accuracy.更多还原