Self-organized fuzzy system generation from training examples

In the synthesis of a fuzzy system two steps are generally employed: the identification of a structure and the optimization of the parameters defining it. The paper presents a methodology to automatically perform these two steps in conjunction using a three-phase approach to construct a fuzzy system from numerical data. Phase 1 outlines the membership functions and system rules for a specific structure, starting from a very simple initial topology. Phase 2 decides a new and more suitable topology with the information received from the previous step; it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located. This, in turn, decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased. Phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set. The accuracy and complexity of the fuzzy system derived by the proposed self-organized fuzzy rule generation procedure (SOFRG) are studied for the problem of function approximation. Simulation results are compared with other methodologies such as artificial neural networks, neuro-fuzzy systems, and genetic algorithms.