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Rough set theory has been successfully applied to vague and uncertain data due to its approximation ability. Matroid is a sophisticated mathematical structure to provide a unifying abstract treatment for graph theory, linear algebra, and combinatorial optimization. In this paper, we redefine rough approximation operators through matroidal approaches and build a matroidal structure of rough set theory...
Attribute reduction is an important issue in rough sets. It has been widely used in pattern recognition, machine learning and data mining. Many mathematical theories, such as fuzzy sets, lattice and matrix, have been applied to study the issue for constructing more effective reduction algorithms. In this paper, the attribute reduction in the decision system is conducted under matroid theory. The matroid...
In the studies on covering-based rough sets, there are few discussions about the relation between a covering-element and objects in the covering-element. But it is actually a significant problem. In this paper, we give some better studies on the refinement of covering. Based on the refinement, some important concepts such as minimal description and neighborhood in covering-based rough sets are discussed...
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