A new rule reduction method for finding interpretable and small rule bases in high dimensional search spaces

Abstract

In the field of fuzzy modeling, fuzzy control and fuzzy classification, the transparency and comprehensibility of a rule base depends essentially on two aspects: the local relevance of the individual rules and the compactness of the rule base with respect to the number of rules. Additionally, in most applications a certain quality of the input/output behavior has to be achieved. This leads to a multicriteria optimization problem and the global optimum can only be reached for small problem sizes. A possible solution to this problem is a two-step approach. In the first step, a set of relevant rules is incrementally collected. In the second step, the number of relevant rules is reduced to a rule base as small as possible. We present an optimizing conflict reduction, based on a genetic algorithm with bottom-up initialization. The aim is to reach a suitable compromise between the modeling error and the number of rules. Our two-step approach does not aim at locating the global optimum, but at finding a satisfying solution in an acceptable time, even in high dimensional search spaces. In contrast to known approaches, this approach allows rule bases with several ten thousand rules to be handled successfully. The results are illustrated for a benchmark problem and are compared with results of other rule reduction methods.