Normal forms for fuzzy logic functions

Abstract

Three types of normal forms are introduced for fuzzy logic functions: disjunctive, conjunctive and additive. Disjunctive and conjunctive normal forms are considered in two variants: infinite and finite. It is shown that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for any L-valued function where L is a support set of any complete BL-algebra. The additive normal form "lies" in the middle of the two others. For all of them the estimation of the quality of approximation is suggested.