Fuzzy clustering of fuzzy systems

A fuzzy system entirely characterizes one region of the input-output product space S = U × V through a relation expressed by a set of fuzzy rules. Effectively, the fuzzy system establishes a fuzzy map, which assigns for each input fuzzy set in U an output fuzzy set in V. The partition of this product space may be made through the decomposition of the relation. The fuzzy clustering of fuzzy rules, here proposed, as well as clustering of data, leads to a fuzzy partition of the S space. The result is a set of fuzzy sub-systems, one for each cluster that will be conveniently linked in a new structure. This paper proposes a new recursive clustering algorithm for the partition of a fuzzy system into a hierarchical collaborative structure. The global response of the hierarchical collaborative structure is identical to the input fuzzy system.