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The embedding of the formal concept analysis into the L-Fuzzy concept theory.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1998)

Mathware and Soft Computing

In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal...

The essential cover and the absolute cover of a schematic space

Wolfgang Rump, Yi Chuan Yang (2009)

Colloquium Mathematicae

A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component,...

The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks

Zdena Riečanová (2008)

Kybernetika

Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which...

The exocenter and type decomposition of a generalized pseudoeffect algebra

David J. Foulis, Silvia Pulmannová, Elena Vinceková (2013)

Discussiones Mathematicae - General Algebra and Applications

We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend...

The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

Klaus Denecke, Jennifer Hyndman, Shelly L. Wismath (2000)

Discussiones Mathematicae - General Algebra and Applications

Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.

The globals of pseudovarieties of ordered semigroups containing B 2 and an application to a problem proposed by Pin

Jorge Almeida, Ana P. Escada (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B 2 , under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3 / 2 of Straubing-Thérien’s concatenation hierarchy has infinite vertex rank.

The globals of pseudovarieties of ordered semigroups containing B2 and an application to a problem proposed by Pin

Jorge Almeida, Ana P. Escada (2010)

RAIRO - Theoretical Informatics and Applications

Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup B2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.

Currently displaying 61 – 80 of 304