Group actions on Cartesian powers with applications to represenation theory.
Ideal systems of intersection and product type
Ideals of weakly associative lattices and pseudo-ordered sets
Interior and closure operators on bounded commutative residuated l-monoids
Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras...
Interior and closure operators on bounded residuated lattices
Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated...
Interior and Closure Operators on Commutative Bounded Residuated Lattices
Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.
Invariance groups of finite functions and orbit equivalence of permutation groups
Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections...
Isomorphismen von Kontexten und Konzeptualverbänden
Konzepte in den triadischen Kontext
Lattice socles and radicals described by a Galois connnection
Lattices of convex equivalences
Les termes : un modèle algébrique de représentation et de structuration de données symboliques
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...
Mathematical morphology and poset geometry.
Matrices ordonnables : une étude algébrique
Modal operators on ordered sets
Multiplicative closed maps on the set of S-subsets of an S-set.
MV-algebras with additive closure operators
N-anti-exchange closure operators
On a characterization of the lattice of -ideals of an ordered set
On algebraic closures of compact elements