Formation of Hierarchical Fuzzy Rule Systems

Many fuzzy rule induction algorithms have been pro-posed in the past. Most of them tend to generate too many rules tbJring the learning process. This is due to data sets obtained from real world systems containing distorted el-ements or noisy data. Most approaches try to completely ignore outliers, which can be potentially hannful since the exmnple may describe a rare but still extremely interest-ing phenomena in the data. In order to avoid this con-flict, we propose to build a hierarrhy of fuzzy rule systems. The goal of this model-hierarchy are interpretable models with only few relevant rules on each level of the hierarchy. The resulting fuzzy model hierarchy forms a structure in which the top model covers all data explicitly and gener-ates a significant smaller number of rules than the original. fuzzy rule learner. The models on the bottom. on the other hand, consist of only a few rules in each level and explain parts with only weak relevance in the data. We demon-strate the proposed method's usefulness on several classi-fication benchmark data sets. The results demonstrate how the rule hierarrhy allows to build much smaller fuzzy rule systems and how the model-especially at higher levels of the hierarchy-remains interpretable.