Optimization of fuzzy systems by approximation of fuzzy relations

A novel approach to the optimization of discretized fuzzy systems is proposed. This method does not require the prespecification of reference fuzzy sets. Instead, the reference fuzzy sets are parameterized and the optimal parameters are obtained by the method of steepest descent. The optimization algorithm is derived based on a theorem which establishes a common input/output description for the approximated and approximating systems. Proof of the required theorem and derivation of the optimization algorithm is fully described. Preliminary simulation results are also presented to illustrate the proposed approach