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Rough set approximations based on a matroidal structure over three sets

Rough set approximations based on a matroidal structure over three sets Pawlak’s classical model of rough set approximations provides an efficient tool for extracting information exactly by employing available knowledge (i.e., known knowledge) in an information system, since many problems in rough set theory are NP-hard and their solution process is therefore greedy and approximate. Many extensions of Pawlak’s classical model have been proposed in recent years. Most of them are considered over one or two sets, that is, one- or two-dimensional space or one- or two-dimensional data. Aided by relation-based rough set models, a few of these extensions are considered over three sets. However, the real world is in three-dimensional space. Therefore, it is necessary to solve these problems with other models, such as covering rough set models. For this purpose, we propose the TP-matroid—a matroidal structure over three sets. Employing the family of feasible sets of a TP-matroid as the available knowledge, a pair of rough set approximations—lower and upper approximations—is provided. In addition, for an information system defined over three sets, assisted by formal concept analysis, we establish a pair of rough set approximations. Furthermore, two TP-matroids are established based on the above pair of rough set approximations. The integration between the two pairs of rough set approximations presented here is discussed. The results show that for an information system in three-dimensional space, the rough set approximations provided here can effectively explore unknown knowledge by using available knowledge based on the family of feasible sets of a TP-matroid. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Intelligence Springer Journals

Rough set approximations based on a matroidal structure over three sets

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0924-669X
eISSN
1573-7497
DOI
10.1007/s10489-022-04144-5
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Abstract

Pawlak’s classical model of rough set approximations provides an efficient tool for extracting information exactly by employing available knowledge (i.e., known knowledge) in an information system, since many problems in rough set theory are NP-hard and their solution process is therefore greedy and approximate. Many extensions of Pawlak’s classical model have been proposed in recent years. Most of them are considered over one or two sets, that is, one- or two-dimensional space or one- or two-dimensional data. Aided by relation-based rough set models, a few of these extensions are considered over three sets. However, the real world is in three-dimensional space. Therefore, it is necessary to solve these problems with other models, such as covering rough set models. For this purpose, we propose the TP-matroid—a matroidal structure over three sets. Employing the family of feasible sets of a TP-matroid as the available knowledge, a pair of rough set approximations—lower and upper approximations—is provided. In addition, for an information system defined over three sets, assisted by formal concept analysis, we establish a pair of rough set approximations. Furthermore, two TP-matroids are established based on the above pair of rough set approximations. The integration between the two pairs of rough set approximations presented here is discussed. The results show that for an information system in three-dimensional space, the rough set approximations provided here can effectively explore unknown knowledge by using available knowledge based on the family of feasible sets of a TP-matroid.

Journal

Applied Intelligence – Springer Journals

Published: Jun 1, 2023

Keywords: Rough set approximations; TP-matroid; Covering; Three sets; Semiconcept

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