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The characterizations of upper approximation operators based on special coverings

100%
Wang P., Li Q.
Open Mathematics
|
2017
|
tom 15
|
nr 1
193-202
EN
In this paper, we discuss the approximation operators [...] apr¯NS ${\overline {apr} _{NS}}$ and [...] apr¯S ${\overline {apr} _S}$ which are based on NS(U) and S. We not only obtain some properties of NS(U) and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.
2
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Interior and closure operators on bounded residuated lattices

100%
Rachůnek J., Svoboda Z.
Open Mathematics
|
2014
|
tom 12
|
nr 3
534-544
EN
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 lattices of their regular elements.
3
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Closure Operators on Complete Almost Distributive Lattices-III

88%
Rao C. R., Undurthi V., Department of Mathematics A. U., gcraomaths@yahoo.co.in, venumaths@yahoo.com
Bulletin of the Section of Logic
|
2015
|
tom 44
|
nr 1-2
EN
In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ(L) to be complemented.
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