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Normal forms in BL and ŁΠ algebras of functions

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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.

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  1. University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30.dubna 22, 701 03, Ostrava 1, Czech Republic

    I. Perfilieva

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  1. I. Perfilieva
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Correspondence to I. Perfilieva.

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Perfilieva, I. Normal forms in BL and ŁΠ algebras of functions. Soft Computing 8, 291–298 (2004). https://doi.org/10.1007/s00500-003-0274-2

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  • DOI: https://doi.org/10.1007/s00500-003-0274-2

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