Title :
Normal forms for fuzzy logic functions
Author :
Perfilieva, Irina
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.
Keywords :
Boolean algebra; fuzzy logic; BL-algebra; L-valued function; additive normal form; conjunctive normal form; disjunctive normal form; finite normal form; fuzzy logic function; infinite normal form; universal approximation formula; universal representation formula; Boolean algebra; Fuzzy logic; Fuzzy sets; Lattices; Logic functions; Neural networks; Prototypes;
Conference_Titel :
Multiple-Valued Logic, 2003. Proceedings. 33rd International Symposium on
Print_ISBN :
0-7695-1918-0
DOI :
10.1109/ISMVL.2003.1201385
