Fuzzy sets of rules for system identification

The synthesis of fuzzy systems involves the identification of a structure and its specialization by means of parameter optimization. In doing this, symbolic approaches which encode the structure information in the form of high-level rules allow further manipulation of the system to minimize its complexity, and possibly its implementation cost, while all-parametric methodologies often achieve better approximation performance. In this paper, we rely on the concept of a fuzzy set of rules to tackle the rule induction problem at an intermediate level. An online adaptive algorithm is developed which almost surely learns the extent to which inclusion of a rule in the rule set significantly contributes to the reproduction of the target behavior. Then, the resulting fuzzy set of rules can be defuzzified to give a conventional rule set with similar behavior. Comparisons with high-level and low-level methodologies show that this approach retains the most positive features of both.