On input space clustering by fuzzy systems and neural networks

A fuzzy system is approximated by a feedforward sigmoidal network by simulating a manifold of an input-output product space of the fuzzy system, where network parameters are adjusted by an optimization algorithm. It is shown that, when such an approximation takes place, both systems share similar dynamical characteristics in which an input space is transformed into an output space by clustering the input space and interpolating among clusters. In fuzzy systems, the input space is clustered by the first layer of the network. The issue of the number of network intermediate nodes necessary to approximate a given fuzzy system is discussed