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Geometric Lattice Structure of Covering-Based Rough Sets through Matroids
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-18
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
Covering-based rough set theory is a useful tool to deal with inexact, uncertain, or vague knowledge in information systems.
Geometric lattice has been widely used in diverse fields, especially search algorithm design, which plays an important role in covering reductions.
In this paper, we construct three geometric lattice structures of covering-based rough sets through matroids and study the relationship among them.
First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by a covering.
Then its characteristics, such as atoms, modular elements, and modular pairs, are studied.
We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets.
Second, we present three sufficient and necessary conditions for two types of covering upper approximation operators to be closure operators of matroids.
We also represent two types of matroids through closure axioms and then obtain two geometric lattice structures of covering-based rough sets.
Third, we study the relationship among these three geometric lattice structures.
Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices.
In a word, this work points out an interesting view, namely, geometric lattice, to study covering-based rough sets.
American Psychological Association (APA)
Huang, Aiping& Zhu, William. 2012. Geometric Lattice Structure of Covering-Based Rough Sets through Matroids. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-993053
Modern Language Association (MLA)
Huang, Aiping& Zhu, William. Geometric Lattice Structure of Covering-Based Rough Sets through Matroids. Journal of Applied Mathematics No. 2012 (2012), pp.1-25.
https://search.emarefa.net/detail/BIM-993053
American Medical Association (AMA)
Huang, Aiping& Zhu, William. Geometric Lattice Structure of Covering-Based Rough Sets through Matroids. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-993053
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993053