Fuzzy rule extraction from input/output data

This paper discusses the question how the membership functions in a fuzzy rule based system can be extracted without human interference. There are several training algorithms, which have been developed initially for neural networks and can be adapted to fuzzy systems. Other algorithms for the extraction of fuzzy rules are inspired by biological evolution. In this paper one of the most successful neural networks training algorithm, the Levenberg-Marquardt algorithm, is discussed, and a very novel evolutionary method, the so-called “bacterial algorithm”, are introduced. The class of membership functions investigated is restricted to the trapezoidal one as it is general enough for practical applications and is anyway the most widely used one. The method can be easily extended to arbitrary piecewise linear functions as well. Apart from the neural networks and evolutional algorithms, fuzzy clustering has also been used for rule extraction. One of the clustering-based rule extraction algorithms that works on the projection of data is also reported in the paper