Incremental neuro-fuzzy systems

The poor scaling behavior of grid-partitioning fuzzy systems in case of increasing data dimensionality suggests using fuzzy systems with a scatter-partition of the input space. Jang has shown that zero-order Sugeno fuzzy systems are equivalent to radial basis function networks (RBFNs). Methods for finding scatter partitions for RBFNs are available, and it is possible to use them for creating scatter-partitioning fuzzy systems. A fundamental problem, however. is the structure identification problem, i.e., the determination of the number of fuzzy rules and their positions in the input space. The supervised growing neural gas method uses classification or regression error to guide insertions of new RBF units. This leads to a more effective positioning of RBF units (fuzzy rule IF-parts, resp.) than achievable with the commonly used unsupervised clustering methods. Example simulations of the new approach are shown demonstrating superior behavior compared with grid-partitioning fuzzy systems and the standard RBF approach of Moody and Darken.