A Genetic Algorithm for Structural and Parametrical Tuning of Fuzzy Systems

In most Fuzzy System applications the structure of the system is chosen non-systematically by an expert according to his knowledge. Nevertheless the system parameters are rich enough to ensure the desired behavior. In the following, we introduce an automatic learning algorithm by de nition of a 1) well behaved and 2) minimal Fuzzy System. A Genetic Algorithm is used to estimate the Fuzzy Systems which capture the above two desired properties best. In contrast to other known approaches where only parametrical tuning takes place, here optimization of the entropy of the fuzzy rule base leads to a minimal number of rules, of membership functions and of subpremises together with an optimal input/output behavior. The resulting Fuzzy System is comparable to systems designed by an expert but with a better performance. Our algorithm is compared to others by a standard benchmark (a system identi cation process) and di erent results for symmetric and non-symmetric membership functions are presented.