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M V -test spaces versus M V -algebras

Antonio Di Nola, Anatolij Dvurečenskij (2004)

Czechoslovak Mathematical Journal

In analogy with effect algebras, we introduce the test spaces and M V -test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between M V -algebras and M V -test spaces.

Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Martin Kalina (2010)

Kybernetika

If element z of a lattice effect algebra ( E , , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a subdirect product of irreducible effect algebras ([18]). This means that if there exists a MacNeille completion E ^ of E which is its extension...

Many-dimensional observables on Łukasiewicz tribe: constructions, conditioning and conditional independence

Tomáš Kroupa (2005)

Kybernetika

Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on σ -algebras of sets. A Łukasiewicz tribe is a collection of fuzzy sets which is closed under the standard fuzzy complementation and under the pointwise application of the Łukasiewicz t-norm to countably many fuzzy sets. An observable is a fuzzy set-valued mapping defined on a σ -algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous...

Maximal completion of a pseudo MV-algebra

Ján Jakubík (2003)

Archivum Mathematicum

In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo M V -algebras.

Maximal MV-algebras.

Alexandru Filipoiu, George Georgescu, Ada Lettieri (1997)

Mathware and Soft Computing

In this paper we define maximal MV-algebras, a concept similar to the maximal rings and maximal distributive lattices. We prove that any maximal MV-algebra is semilocal, then we characterize a maximal MV-algebra as finite direct product of local maximal MV-algebras.

Median prime ideals of pseudo-complemented distributive lattices

M. Sambasiva Rao (2022)

Archivum Mathematicum

Coherent ideals, strongly coherent ideals, and τ -closed ideals are introduced in pseudo-complemented distributive lattices and their characterization theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which...

Metric-fine uniform frames

Joanne L. Walters-Wayland (1998)

Commentationes Mathematicae Universitatis Carolinae

A locallic version of Hager’s metric-fine spaces is presented. A general definition of 𝒜 -fineness is given and various special cases are considered, notably 𝒜 = all metric frames, 𝒜 = complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.

Metrizability of σ -frames

M. Mehdi Ebrahimi, M. Vojdani Tabatabaee, M. Mahmoudi (2004)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Metrizable completely distributive lattices

Zhang De-Xue (1997)

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.

Modal operators on bounded residuated l -monoids

Jiří Rachůnek, Dana Šalounová (2008)

Mathematica Bohemica

Bounded residuated lattice ordered monoids ( R -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 and...

Modal operators on MV-algebras

Magdalena Harlenderová, Jiří Rachůnek (2006)

Mathematica Bohemica

Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated.

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