A new universal approximation result for fuzzy systems, which reflects CNF DNF duality
✍ Scribed by Irina Perfilieva; Vladik Kreinovich
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 103 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0884-8173
No coin nor oath required. For personal study only.
✦ Synopsis
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) Յ 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) Յ R DNF ( x, y) holds. Such existence is proved in our paper.