STRUCTURE AND APPROXIMATION OF A MULTIDIMENSIONAL PIECEWISE LINEAR FUNCTION BASED ON THE INPUT SPACE OF SUBDIVISION FUZZY SYSTEMS
Peng Weilin · Xitong kexue yu shuxue · 2014
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 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 u-integrable function.The results show that the approximation ability of the piecewise hnear functions for a continuous function can be extended to general integrable function in fuzzy systems.