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Left and right semi-uninorms on a complete lattice

Yong Su, Zhudeng Wang, Keming Tang (2013)

Kybernetika

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...

Les termes : un modèle algébrique de représentation et de structuration de données symboliques

Marie-Catherine Daniel-Vatonne, Colin de la Higuera (1993)

Mathématiques et Sciences Humaines

Nos travaux se situent dans le cadre de l'analyse conceptuelle des données. Notre objectif est de généraliser les représentations par variables binaires ou nominales en y adjoignant la modélisation de structures internes. Le problème est de ne pas perdre en complexité algorithmique ce qui est gagné en puissance de représentation. Selon ces considérations, décrire les données et des classes de données par des structures arborescentes semble un bon compromis. Le système de représentation que nous...

Lexico extension and a cut completion of a half l-group

Štefan Černák, Milan Demko (2002)

Discussiones Mathematicae - General Algebra and Applications

The cut completi on of an hl-group G with the abelian increasing part is investigated under the assumption that G is a lexico extension of its hl-subgroup.

Lexicographic extensions of dually residuated lattice ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Mathematica Bohemica

Dually residuated lattice ordered monoids ( D R ℓ -monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ( M V -algebras, B L -algebras) and their non-commutative variants ( G M V -algebras, pseudo B L -algebras). In the paper, lex-extensions and lex-ideals of D R ℓ -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.

Lexicographic product decompositions of half linearly ordered loops

Milan Demko (2007)

Czechoslovak Mathematical Journal

In this paper we prove for an hl-loop Q an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop Q with a finite number of lexicographic factors have isomorphic refinements.

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