![](/images/graphics-bg.png)
Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory
Joint Authors
Zhu, William
Tang, Jianguo
She, Kun
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-27, 27 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-07-26
Country of Publication
Egypt
No. of Pages
27
Main Subjects
Abstract EN
Constructing structures with other mathematical theories is an important research field of rough sets.
As one mathematical theory on sets, matroids possess a sophisticated structure.
This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets.
In order to understand intuitively the relationships between these two theories, we study this problem from the viewpoint of graph theory.
Therefore, any partition of the universe can be represented by a family of complete graphs or cycles.
Then two different kinds of matroids are constructed and some matroidal characteristics of them are discussed, respectively.
The lower and the upper approximations are formulated with these matroidal characteristics.
Some new properties, which have not been found in rough sets, are obtained.
Furthermore, by defining the concept of lower approximation number, the rank function of some subset of the universe and the approximations of the subset are connected.
Finally, the relationships between the two types of matroids are discussed, and the result shows that they are just dual matroids.
American Psychological Association (APA)
Tang, Jianguo& She, Kun& Zhu, William. 2012. Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-27.
https://search.emarefa.net/detail/BIM-993897
Modern Language Association (MLA)
Tang, Jianguo…[et al.]. Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory. Journal of Applied Mathematics No. 2012 (2012), pp.1-27.
https://search.emarefa.net/detail/BIM-993897
American Medical Association (AMA)
Tang, Jianguo& She, Kun& Zhu, William. Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-27.
https://search.emarefa.net/detail/BIM-993897
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993897