Matroidal Structure of Rough Sets Based on Serial and Transitive Relations
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-04
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe.
It has been applied to machine learning, knowledge discovery, and data mining.
The theory of matroids is a generalization of linear independence in vector spaces.
It has been used in combinatorial optimization and algorithm design.
In order to take advantages of both rough sets and matroids, in this paper we propose a matroidal structure of rough sets based on a serial and transitive relation on a universe.
We define the family of all minimal neighborhoods of a relation on a universe and prove it satisfies the circuit axioms of matroids when the relation is serial and transitive.
In order to further study this matroidal structure, we investigate the inverse of this construction: inducing a relation by a matroid.
The relationships between the upper approximation operators of rough sets based on relations and the closure operators of matroids in the above two constructions are studied.
Moreover, we investigate the connections between the above two constructions.
American Psychological Association (APA)
Liu, Yanfang& Zhu, William. 2012. Matroidal Structure of Rough Sets Based on Serial and Transitive Relations. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-993255
Modern Language Association (MLA)
Liu, Yanfang& Zhu, William. Matroidal Structure of Rough Sets Based on Serial and Transitive Relations. Journal of Applied Mathematics No. 2012 (2012), pp.1-16.
https://search.emarefa.net/detail/BIM-993255
American Medical Association (AMA)
Liu, Yanfang& Zhu, William. Matroidal Structure of Rough Sets Based on Serial and Transitive Relations. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-993255
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993255