Open Access
Translator Disclaimer
2013 Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets
Shiping Wang, Qingxin Zhu, William Zhu, Fan Min
J. Appl. Math. 2013: 1-7 (2013). DOI: 10.1155/2013/519173


Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, corresponding problems in graphs are also transformed into ones in covering-based rough sets. For example, finding a minimal edge cover of a graph is translated into finding a minimal general reduct of a covering. The main contributions of this paper are threefold. First, any graph is converted to a covering. Two graphs induce the same covering if and only if they are isomorphic. Second, some new concepts are defined in covering-based rough sets to correspond with ones in graph theory. The upper approximation number is essential to describe these concepts. Finally, from a new viewpoint of covering-based rough sets, the general reduct is defined, and its equivalent characterization for the edge cover is presented. These results show the potential for the connection between covering-based rough sets and graphs.


Download Citation

Shiping Wang. Qingxin Zhu. William Zhu. Fan Min. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets." J. Appl. Math. 2013 1 - 7, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1283.05227
Digital Object Identifier: 10.1155/2013/519173

Rights: Copyright © 2013 Hindawi


Vol.2013 • 2013
Back to Top