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.

A Fuzzy Method for Learning Simple Boolean Formulas from Examples / B. Apolloni, A. Brega, D. Malchiodi, C. Orovas, A.M. Zanaboni - In: Computational Intelligence for Modelling and Prediction / Saman K. Halgamuge, Lipo Wang. - Berlin : Springer, 2005. - ISBN 3540260714. - pp. 367-382

### A Fuzzy Method for Learning Simple Boolean Formulas from Examples

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
Settore INF/01 - Informatica
2005
Book Part (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
##### Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/9343`
• ND
• ND
• ND