F. Bergadano et V. Cutello, PROBABLY APPROXIMATELY CORRECT LEARNING IN FUZZY CLASSIFICATION SYSTEMS, IEEE transactions on fuzzy systems, 3(4), 1995, pp. 473-478
An efficient method for learning (trapezoidal) membership functions fo
r fuzzy predicates is presented. Positive and negative examples of one
class are given together with a system of classification rules. The l
earned membership functions can be used for the fuzzy predicates occur
ring in the given rules to classify further examples. We show that the
obtained classification is approximately correct with high probabilit
y. This justifies the obtained fuzzy sets within one particular classi
fication problem, instead of relying on a subjective meaning of fuzzy
predicates as normally done by a domain expert.