Fuzzy modeling by hierarchically built fuzzy rule bases

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 identi®cation 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 sub-problems with smooth transitions between them. In order to develop this class of models, we ®rst 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 ¯exibilization will allow us to have fuzzy rules with di€erent degrees of speci®city, and thus to improve the mod-eling of those problem subspaces where the former models have bad performance, as a re®nement. This approach allows us not to have to assume a ®xed number of rules and to integrate the good local behavior of the hierarchical model with the global model, ensuring a good global performance.