Fuzzy modeling by hierarchically built fuzzy rule bases

Abstract

Although Mamdani-type fuzzy rule-based systems (FRBSs) became successfully performing clearly interpretable fuzzy models, they still have some lacks related to their accuracy when solving complex problems. A variant of these kinds of systems, which allows to perform a more accurate model representation, are the so-called approximate FRBSs. This alternative representation still cannot avoid the problems concerning the fuzzy rule learning methods, which as prototype identification algorithms, try to extract those approximate rules from the object problem space. In this paper we deal with the previous problems, viewing fuzzy models as a class of local modeling approaches which attempt to solve a complex problem by decomposing it into a number of simpler subproblems with smooth transitions between them. In order to develop this class of models, we first propose a common framework to characterize available approximate fuzzy rule learning methods, and later we modify it by introducing a fuzzy rule base hierarchical learning methodology (FRB-HLM). This methodology is based on the extension of the simple building process of the fuzzy rule base of FRBSs in a hierarchical way, in order to make the system more accurate. This flexibilization will allow us to have fuzzy rules with different degrees of specificity, and thus to improve the modeling of those problem subspaces where the former models have bad performance, as a refinement. This approach allows us not to have to assume a fixed number of rules and to integrate the good local behavior of the hierarchical model with the global model, ensuring a good global performance.