Journal of Applied Mathematics

Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory

Jianguo Tang, Kun She, and William Zhu

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 973920, 27 pages.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357153525

Digital Object Identifier
doi:10.1155/2012/973920

Mathematical Reviews number (MathSciNet)
MR2984189

Zentralblatt MATH identifier
1259.03069

Citation

Tang, Jianguo; She, Kun; Zhu, William. Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory. J. Appl. Math. 2012 (2012), Article ID 973920, 27 pages. doi:10.1155/2012/973920. https://projecteuclid.org/euclid.jam/1357153525


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