Displaying similar documents to “Local bounded commutative residuated ℓ -monoids”

Interior and closure operators on bounded residuated lattice ordered monoids

Filip Švrček (2008)

Czechoslovak Mathematical Journal

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G M V -algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior G M V -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on D R l -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on G M V -algebras.

Negation in bounded commutative D R ℓ -monoids

Jiří Rachůnek, Vladimír Slezák (2006)

Czechoslovak Mathematical Journal

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The class of commutative dually residuated lattice ordered monoids ( D R ℓ -monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded D R ℓ -monoids is introduced, its properties are studied and the sets of regular and dense elements of D R ℓ -monoids are described.

A duality between algebras of basic logic and bounded representable D R l -monoids

Jiří Rachůnek (2001)

Mathematica Bohemica

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B L -algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that B L -algebras are the duals of bounded representable D R l -monoids. This duality enables us to describe some structure properties of B L -algebras.