ALGORITHMIC ASPECTS OF FUZZY CONTROL

Fuzzy control is at present still the most important application of fu zzy theory. It is a generalized form of expert control using fuzzy set s in the definition of vague/linguistic predicates, modeling a system by If...then rules. In the classical approaches (Zadeh, Mamdani) the e ssential idea is that a fact (observation) known concerning the actual state of the system will match with one or several rules in the model to some positive degree, the conclusion will be calculated by the eva luation of the degree of these matches, and the marched rules themselv es. In these approaches, the rules contain linguistic terms, i.e., fuz zy sets in the consequent parts, and these terms, weighted with their respective degrees of matching, will be combined in order to obtain a fuzzy conclusion-from which the crisp action is obtained by defuzzific ation, as e.g. the center of gravity method. This paper summarizes the se classical methods and turns attention to their weak point: the comp utational complexity aspect As a partial solution, the use of sparse r ule bases is proposed and rule interpolation as a fitting inference en gine is presented. The problem of preserving or not preserving lineari ty is discussed when terms in the rules are restricted to piecewise li near.