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On rough approximations via ideal
Faculty
Science
Year:
2013
Type of Publication:
Article
Pages:
114-125
Authors:
Tantawy, O. A. E, Mustafa, Heba. I
DOI:
10.1016/j.ins.2013.05.012
Journal:
INFORMATION SCIENCES ELSEVIER SCIENCE INC
Volume:
251
Research Area:
Computer Science
ISSN
ISI:000325120800008
Keywords :
Complete atomic Boolean lattice, Lower and upper approximations via ideal, Extensive, symmetric, and closed mappings
Abstract:
In this paper, we generalize the rough set model by defining new approximation operators in more general setting of a complete atomic Boolean lattice by using an ideal. An ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under finite unions. We introduce the concept of lower and upper approximations via ideal in a lattice theoretical setting. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. Also properties of the ordered set of the lower and upper of an element of a complete atomic Boolean lattice via ideal are investigated. We also study the connections between the rough approximations defined by. Jarvinen {[}10,11] and our new approximations. Various examples are given. Finally we give a new approach for defining the rough approximations w.r.t the induced map by using an ideal. We study the connections between the rough approximations defined with respect to the induced map by using an ideal and the rough approximations defined with respect to the considered map under certain conditions of the map. (c) 2013 Elsevier Inc. All rights reserved.
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