Extension of the Levenberg-Marquardt algorithm for the extraction of trapezoidal and general piecewise linear fuzzy rules

Discusses how training algorithms for determining membership functions in fuzzy rule based systems can be applied. There are several training algorithms, which have been developed initially for neural networks and can be adapted to fuzzy systems. In the paper the Levenberg-Marquardt algorithm is introduced, allowing the determination of an optimal rule base and converging faster than some more classic methods. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well