An enhanced two-level Boolean synthesis methodology for fuzzy rules minimization

A new methodology for the minimization of a given set of fuzzy rules is presented. It is based on a novel mapping of fuzzy relations on Boolean functions and exploits existing Boolean synthesis algorithms. In this mapping each fuzzy membership predicate is translated into a Boolean variable and proper constraints on Boolean manipulations are added to guarantee fuzziness translation. The formal consistency of the approach depends on a fuzzy semantic which easily generalizes most of the existing models, granting broad applicability to the suggested procedure. The applicability of an enhanced two-level Boolean minimizer is demonstrated, and the technique is applied to the fuzzy identification of nonlinear systems, consistently reducing the number of rules and easing application of further optimization interventions