Fuzzy System and CMAC Network with B-Spline Membership/Basis Functions can Approximate A Smooth Function and its Derivatives
Shitong Wang, Hongjun Lü · International Journal of Computational Intelligence and Applications · 2003
In control and other modeling applications, fuzzy system with B-spline membership functions and CMAC neural network with B-spline basis functions are sometimes desired to approximate not only the assigned smooth function as well as its derivatives. In this paper, by designing the fuzzy system and CMAC neural network with B-spline basis functions, we prove that such a fuzzy system and CMAC can universally approximate a smooth function and its derivatives, that is to say, for a given accuracy, we can approximate an arbitrary smooth function by such fuzzy system and CMAC that not only the function is approximated within this accuracy, but its derivatives are approximated as well. The conclusions here provide solid theoretical foundation for their extensive applications.