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International Journal of Machine Learning and Cybernetics
Erschienen in: International Journal of Machine Learning and Cybernetics 3/2014

01.06.2014 | Original Article

Closed-set lattice of regular sets based on a serial and transitive relation through matroids

verfasst von: Qingyin Li, William Zhu

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 3/2014

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Abstract

Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a serial and transitive relation on a universe, the collection of all the regular sets of the generalized rough set is a lattice. In this paper, we use the lattice to construct a matroid and then study relationships between the lattice and the closed-set lattice of the matroid. First, the collection of all the regular sets based on a serial and transitive relation is proved to be a semimodular lattice. Then, a matroid is constructed through the height function of the semimodular lattice. Finally, we propose an approach to obtain all the closed sets of the matroid from the semimodular lattice. Borrowing from matroids, results show that lattice theory provides an interesting view to investigate rough sets.
Vorheriger Artikel A framework for imprecise robust one-class classification models
Nächster Artikel Research on multi-objective linear programming problem with fuzzy coefficients in constraints

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Metadaten
Titel
Closed-set lattice of regular sets based on a serial and transitive relation through matroids
verfasst von
Qingyin Li
William Zhu
Publikationsdatum
01.06.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 3/2014
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-013-0176-2

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