Original Article
Kyungpook Mathematical Journal 2015; 55(3): 549-562
Published online September 23, 2015
Copyright © Kyungpook Mathematical Journal.
Pointless Form of Rough Sets
Abolghasem Karimi Feizabad1 and Ali Akbar Estaji and Mostafa Abedi2
1Department of Mathematics, Gorgan Branch, Islamic Azad University, Gorgan, Iran
2Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran
In this paper we introduce the pointfree version of rough sets. For this we consider a lattice $L$ instead of the power set
$P(X)$ of a set $X$. We study the properties of lower and upper pointfree approximation, precise elements, and their relation with prime elements. Also, we study lower and upper pointfree approximation as a Galois connection, and discuss the relations between partitions and Galois connections
Keywords: rough set, frame, prime element, lower and upper approximations, precise elements, Galois connection