A Multi-Resolution Radial Basis Function Network for Self-Organization, Defuzzification, and Inference in Fuzzy Rule-Based Systems

The merit of fuzzy rule based systems stems from their capability of encoding qualitative knowledge of experts into quantitative rules. Recent advancement in automatic tuning or self-organization of fuzzy rules from experimental data further enhances their power, allowing the integration of the top-down encoding of knowledge with the bottom-up learning of rules. In this paper, methods of self-organizing fuzzy rules and of performing defuzzification and inference is presented based on a multi-resolution radial basis function network. The network learns an arbitrary input-output mapping from sample distribution as the union of hyper-ellipsoidal clusters of various locations, sizes and shapes. The hyper-ellipsoidal clusters, representing fuzzy rules, are self-organized based of global competition in such a way as to ensute uniform mapping errors. The cooperative interpolation among the multiple clusters associated with a mapping allows the network to perform a bidirectional many-to-many mapping, representing a particular from of defuzzification. Finally, an inference engine is constructed for the network to search for an optimal chain of rules or situation transitions under the constraint of transition feasibilities imposed by the learned mapping. Applications of the proposed network to skill acquisition are shown.