It is known that fuzzy systems are universal approximators, i.e., any input-output system can be approximated, within any given accuracy, by a system described by fuzzy rules. Fuzzy rules work well in many practical applications. However, in some applications, the existing fuzzy rule approximation techniques are not sufficient:
First, in many practical problems (e.g., in many control applications), derivatives of the approximated function are very important, and so, we want not only the approximating function to be close to the approximated one, but we also want their derivatives to be close; however, standard fuzzy approximation techniques do not guarantee the accuracy of approximating a derivative.
Second, to get the desired approximation accuracy, we sometimes need unrealistically many rules.
In this talk, we show how both problems can be solved.