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Gaps and dualities in Heyting categories

Jaroslav Nešetřil, Aleš Pultr, Claude Tardif (2007)

Commentationes Mathematicae Universitatis Carolinae

We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.

Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Jan Kühr (2008)

Czechoslovak Mathematical Journal

We deal with unbounded dually residuated lattices that generalize pseudo M V -algebras in such a way that every principal order-ideal is a pseudo M V -algebra. We describe the connections of these generalized pseudo M V -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo M V -algebra A by means of the positive cone of a suitable ℓ -group G A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ -subgroups of G A are isomorphic....

Generalized homogeneous, prelattice and MV-effect algebras

Zdena Riečanová, Ivica Marinová (2005)

Kybernetika

We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra P are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra P is a union of generalized MV-effect algebras and...

Generalized prime D -filters of distributive lattices

A.P. Phaneendra Kumar, M. Sambasiva Rao, K. Sobhan Babu (2021)

Archivum Mathematicum

The concept of generalized prime D -filters is introduced in distributive lattices. Generalized prime D -filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime D -filters is introduced in distributive lattices and properties of minimal prime D -filters are then studied with respect to congruences. Some topological properties of the space of all prime D -filters of a distributive lattice are also studied.

Generalized versions of MV-algebraic central limit theorems

Piotr Nowak, Olgierd Hryniewicz (2015)

Kybernetika

MV-algebras can be treated as non-commutative generalizations of boolean algebras. The probability theory of MV-algebras was developed as a generalization of the boolean algebraic probability theory. For both theories the notions of state and observable were introduced by abstracting the properties of the Kolmogorov's probability measure and the classical random variable. Similarly, as in the case of the classical Kolmogorov's probability, the notion of independence is considered. In the framework...

Generated fuzzy implications and fuzzy preference structures

Vladislav Biba, Dana Hliněná (2012)

Kybernetika

The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet ( p , i , j ) , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.

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