APPROXIMATION ANALYSIS OF NONHOMOGENEOUS LINEAR T-S FUZZY SYSTEM BASED ON GRID PIECEWISE LINEAR FUNCTION STRUCTURE
Wang Hongzh · Xitong kexue yu shuxue · 2015
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.