Approximation of Function and its Derivatives by Fuzzy Systems

This paper presents a fuzzy system-based approach for the approximation of functions with several variables. The improved results on the approximation of regular functions show that fuzzy systems (FS) may keep their semantic structure while approximating, to any degree of accuracy, not only sufficiently regular functions, but also their derivatives. The result is an FS structure containing linguistic relationships of the functions and also of its derivatives approximations. This approach can result in improved numerical methods for solving partial differential equations or be used in optimal or predictive control