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.