Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory

Jianguo Tang, Kun She and William Zhu

Journal of Applied Mathematics, 2012, vol. 2012, 1-27

Abstract:

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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/JAM/2012/973920.pdf (application/pdf)
http://downloads.hindawi.com/journals/JAM/2012/973920.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:973920

DOI: 10.1155/2012/973920

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().