Probably approximately correct learning in fuzzy classification systems

An efficient method for learning (trapezoidal) membership functions for fuzzy predicates is presented. Positive and negative examples of one class are given together with a system of classification rules. The learned membership functions can be used for the fuzzy predicates occurring in the given rules to classify further examples. We show that the obtained classification is approximately correct with high probability. This justifies the obtained fuzzy sets within one particular classification problem, instead of relying on a subjective meaning of fuzzy predicates as normally done by a domain expert