Normal forms in BL and ŁΠ algebras of functions

Authors:
I. Perfilieva
Affiliations:
Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2004

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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 proved 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.