Multi-resolution techniques in the rules-based intelligent control systems: a universal approximation result

One of the main problems of fuzzy control is that the number of rules which are necessary to represent a given control strategy with a given accuracy, grows exponentially with the increase in accuracy. As a result, for reasonable accuracy and a reasonable number of input variables, a great number of rules is sometimes needed. In this paper, we start to solve this problem by pointing out that traditional one-step fuzzy rule bases, in which expert rules directly express control in terms of the input, are often a simplification of the actual multi-step expert reasoning. We show that a natural formalization of such expert reasoning leads to a universal approximation result in which the number of control rules does not increase with the increase in accuracy. Thus, this multi-resolution approach looks like a promising solution to the rule base explosion problem.