Approximation of Derivatives by Fuzzy Systems

Universal approximation is the basis for theoretical research and practical application of fuzzy systems. However, their ability to model static information has been successfully proven and tested, while on the other hand their limitations. In simultaneously modeling dynamical information are well known. So, if a fuzzy model is a correct representation of a process or a function, the derivative of its mathematical expression is not necessarily a derivative fuzzy model of the process or function. In this paper, we propose a non-static fuzzy system that is capable of linguistically modeling both the static and the dynamical information of a modeled system. This results on the approximation of its regular functions being improved, showing that fuzzy systems may keep their semantic structure while approximating to any degree of accuracy not only sufficiently regular functions, but also their derivatives