Displaying similar documents to “Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures”

Negation in bounded commutative D R ℓ -monoids

Jiří Rachůnek, Vladimír Slezák (2006)

Czechoslovak Mathematical Journal

Similarity:

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.

Modal operators on bounded residuated l -monoids

Jiří Rachůnek, Dana Šalounová (2008)

Mathematica Bohemica

Similarity:

Bounded residuated lattice ordered monoids ( R ℓ -monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo MV -algebras (or, equivalently, GMV -algebras) and pseudo BL -algebras (and so, particularly, MV -algebras and BL -algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on MV -algebras were studied by Harlenderová...

Representable dually residuated lattice-ordered monoids

Jan Kühr (2003)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Dually residuated lattice-ordered monoids (DRl-monoids) generalize lattice-ordered groups and include also some algebras related to fuzzy logic (e.g. GMV-algebras and pseudo BL-algebras). In the paper, we give some necessary and sufficient conditions for a DRl-monoid to be representable (i.e. a subdirect product of totally ordered DRl-monoids) and we prove that the class of representable DRl-monoids is a variety.