Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations
Joint Authors
Zhu, William
Liu, Yanfang
Li, Hui
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-05
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems.
Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets.
In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relation.
First, a family of sets are constructed through the lower approximation of a tolerance relation and they are proved to satisfy the circuit axioms of matroids.
Thus we establish a matroid with the family of sets as its circuits.
Second, we study the properties of the matroid including the base and the rank function.
Moreover, we investigate the relationship between the upper approximation operator based on a tolerance relation and the closure operator of the matroid induced by the tolerance relation.
Finally, from a tolerance relation, we can get a matroidof the generalized rough set based on the tolerance relation.
The matroid can also induce a new relation.
We investigate the connection between the original tolerance relation and the induced relation.
American Psychological Association (APA)
Li, Hui& Liu, Yanfang& Zhu, William. 2014. Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1048877
Modern Language Association (MLA)
Li, Hui…[et al.]. Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations. The Scientific World Journal No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-1048877
American Medical Association (AMA)
Li, Hui& Liu, Yanfang& Zhu, William. Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1048877
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1048877