A new universal approximation result for fuzzy systems, which reflects CNF DNF duality

There are two main fuzzy system methodologies for translating expert rules into a logical formula: In Mamdani's methodology, we get a DNF formula (disjunction of conjunctions), and in a methodology which uses logical implications, we get, in effect, a CNF formula (conjunction of disjunctions). For both methodologies, universal approximation results have been proven which produce, for each approximated function f(x), two different approximating relations R_DNF(x, y) and R_CNF(x, y). Since, in fuzzy logic, there is a known relation F_CNF(x) ≤ F_DNF(x) between CNF and DNF forms of a propositional formula F, it is reasonable to expect that we would be able to prove the existence of approximations for which a similar relation R_CNF(x, y) ≤ R_DNF(x, y) holds. Such existence is proved in our paper. © 2002 Wiley Periodicals, Inc.