Abstract
Fuzzy classifier systems are genetic based machine learning systems which integrate a fuzzy rule base, a genetic algorithm and an apportionment of credit function. In this paper we present a Monte-Carlo selection rule which enables us to give a global convergence proof for (fuzzy) classifier systems and thus combines the advantages of genetic algorithms and simulated annealing algorithms. With the help of the representation theorem we define a mapping from a fuzzy rule language to a crisp rule language and we compare the complexity of the resulting crisp and fuzzy classifier systems. We prove that in the context of genetic based machine learning the performance of the fuzzy version is better than the crisp version.
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