Sublattices corresponding to very true operators in commutative basic algebras
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 2
Abstract
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.1 Keywords: commutative basic algebra, very true operator, idempotent operator, relatively complete sublattice. 2010 Mathematics Subject Classification: 06B23, 03G25, 03B45.
Authors and Affiliations
Filip Švrček, Ivan Chajda
Keywords
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