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Rough sets provide an efficient tool for attribute reduction and rule extraction. However, many important problems in rough set theory, including attribute reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. As a generalization of linear independence in vector spaces, matroids have wide applications in diverse fields, particularly in greedy algorithm design. In...
This paper proposes a framework to integrate rough sets with matroids. Specifically, we propose the lower and upper rough matroids which extend the matroid. They are established by the lower and upper approximations of generalized rough sets based on relations, respectively. As a generalization of the lower (upper) rough matroid, the lower (upper) rough greedoid is defined, and it also a generalization...
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