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Open AccessArticle

Four Operators of Rough Sets Generalized to Matroids and a Matroidal Method for Attribute Reduction

1
College of Electrical & Information Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China
2
School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(9), 418; https://doi.org/10.3390/sym10090418
Received: 8 August 2018 / Revised: 13 September 2018 / Accepted: 14 September 2018 / Published: 19 September 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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PDF [780 KB, uploaded 19 September 2018]

Abstract

Rough sets provide a useful tool for data preprocessing during data mining. However, many algorithms related to some problems in rough sets, such as attribute reduction, are greedy ones. Matroids propose a good platform for greedy algorithms. Therefore, it is important to study the combination between rough sets and matroids. In this paper, we investigate rough sets and matroids through their operators, and provide a matroidal method for attribute reduction in information systems. Firstly, we generalize four operators of rough sets to four operators of matroids through the interior, closure, exterior and boundary axioms, respectively. Thus, there are four matroids induced by these four operators of rough sets. Then, we find that these four matroids are the same one, which implies the relationship about operators between rough sets and matroids. Secondly, a relationship about operations between matroids and rough sets is presented according to the induced matroid. Finally, the girth function of matroids is used to compute attribute reduction in information systems. View Full-Text
Keywords: rough set; matroid; operator; attribute reduction rough set; matroid; operator; attribute reduction
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wang, J.; Zhang, X. Four Operators of Rough Sets Generalized to Matroids and a Matroidal Method for Attribute Reduction. Symmetry 2018, 10, 418.

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