# Pointless Form of Rough Sets

• FEIZABADI, ABOLGHASEM KARIMI (Department of Mathematics, Gorgan Branch, Islamic Azad University) ;
• ESTAJI, ALI AKBAR (Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University) ;
• ABEDI, MOSTAFA (Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University)
• Accepted : 2014.05.28
• Published : 2015.09.23
• 37 23

#### Abstract

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

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#### Cited by

1. On the category of rough sets vol.21, pp.9, 2017, https://doi.org/10.1007/s00500-016-2135-9