Function approximation with decomposed fuzzy systems

If the number of input signals increases, a fuzzy system gets increasingly intractable for two reasons. On the one hand the knowledge acquisition suffers increasingly from the knowledge engineering bottleneck. On the other hand, computational and memory demands of fuzzy systems increase strongly, thus suffering from the curse of dimensionality. The first problem is classically addressed by learning techniques, the second by decomposing the fuzzy system. The NetFAN-approach (Network of Fuzzy Adaptive Nodes) combines decomposition with learning in order to apply fuzzy techniques to more complex applications. Different ways to decompose a fuzzy system are discussed in this paper. For the favorite decomposition principle, it is shown to be an universal function approximator, despite decomposition. The real-world example of controlling a pneumatic positioning system finally demonstrates the applicability and benefits of this type of hierarchical decomposition, namely a significantly reduced number of rules.