Journal of Applied Mathematics
Volume 2013 (2013), Article ID 241485, 15 pages
http://dx.doi.org/10.1155/2013/241485
Research Article

Soft Rough Approximation Operators and Related Results

Zhaowen Li,1 Bin Qin,2 and Zhangyong Cai3

1School of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
2School of Information and Statistics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China
3Department of Mathematics, Guangxi Teachers College, Nanning, Guangxi 530023, China

Received 2 August 2012; Revised 21 January 2013; Accepted 22 January 2013

Academic Editor: Hui-Shen Shen

Copyright © 2013 Zhaowen Li et al. 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.

Abstract

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.