Geodesic
Sublattices corresponding to very true operators in commutative basic algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 183-189

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We introduce the concept of very true operator on a commutative basic algebra in a way analogous to that for fuzzy logics. We are motivated by the fact that commutative basic algebras form an algebraic axiomatization of certain non-associative fuzzy logics. We prove that every such operator is fully determined by a certain relatively complete sublattice provided its idempotency is assumed.
Keywords: commutative basic algebra, very true operator, idempotent operator, relatively complete sublattice 
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Chajda, Ivan; Švrček, Filip. Sublattices corresponding to very true operators in commutative basic algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 2, pp. 183-189. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_2_a3/