Sublattices corresponding to very true operators in commutative basic algebras
Ivan Chajda, Filip Švrček (2014)
Discussiones Mathematicae - General Algebra and Applications
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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.