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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 486321, 11 pages
Research Article

Soft Rough Approximation Operators on a Complete Atomic Boolean Lattice

Mathematics Department, Faculty of Science, Zagazig University, Egypt

Received 23 May 2013; Revised 3 August 2013; Accepted 4 August 2013

Academic Editor: Sotiris Ntouyas

Copyright © 2013 Heba I. Mustafa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The concept of soft sets based on complete atomic Boolean lattice, which can be seen as a generalization of soft sets, is introduced. Some operations on these soft sets are discussed, and new types of soft sets such as full, keeping infimum, and keeping supremum are defined and supported by some illustrative examples. Two pairs of new soft rough approximation operators are proposed and the relationship among soft set is investigated, and their related properties are given. We show that Järvinen's approximations can be viewed as a special case of our approximation. If , then our soft approximations coincide with crisp soft rough approximations (Feng et al. 2011).