A Fuzzy Method for Learning Simple Boolean Formulas from Examples

We discuss a method for inferring Boolean functions from examples. The method is inherently fuzzy in two respects: i) we work with a pair of formulas representing rough sets respectively included by and including the support of the goal function, and ii) we manage the gap between the sets for simplifying their expressions. Namely, we endow the gap with a couple of membership functions of its elements to the set of positive and negative points of the goal function and balance the fuzzy broadening of the sets. This gives the benefit of describing them with a shorter number of symbols for a better understandability of the formulas. The cost-benefit trade-off is obtained via a simulated annealing procedure equipped with special backtracking facilities. We tested the method on both an ad hoc case study and a well known benchmark found on the web.