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• W2063702913 abstract "Covering is a common form of data representation, and covering-based rough sets serve as an efficient technique to process this type of data. However, many important problems such as covering reduction in covering-based rough sets are NP-hard so that most algorithms to solve them are greedy. Matroids provide well-established platforms for greedy algorithm foundation and implementation. Therefore, it is necessary to integrate covering-based rough set with matroid. In this paper, we propose four matroidal structures of coverings and establish their relationships with rough sets. First, four different viewpoints are presented to construct these four matroidal structures of coverings, including 1-rank matroids, bigraphs, upper approximation numbers and transversals. The respective advantages of these four matroidal structures to rough sets are explored. Second, the connections among these four matroidal structures are studied. It is interesting to find that they coincide with each other. Third, a converse view is provided to induce a covering by a matroid. We study the relationship between this induction and the one from a covering to a matroid. Finally, some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures. These interesting results demonstrate the potential to combine covering-based rough sets with matroids. • Four matroidal structures of a covering are proposed from four different viewpoints. • The connections among these four matroidal structures are studied. • Induction of a covering by a matroid and its relationship with induction of a matroid by a covering. • Some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures." @default.
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• W2063702913 date "2013-11-01" @default.
• W2063702913 modified "2023-10-16" @default.
• W2063702913 title "Four matroidal structures of covering and their relationships with rough sets" @default.
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• W2063702913 doi "https://doi.org/10.1016/j.ijar.2013.07.001" @default.
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