Intelligent control is a very successful method of transforming expert knowledge of control rules (formulated in terms of natural language, like "small") into a precise control strategy. It has led to many spectacular applications, ranging from appliances to automatic subway control to super-precise temperature control on a Space Shuttle mission.
It is known that fuzzy control is a universal approximator, i.e., that it can approximate every possible control strategy within an arbitrary accuracy. 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 variable, we sometimes need astronomically many rules.
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.