【摘 要】
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To study with other mathematical theories is an important research direction of rough sets. And this not only enrich the study of rough sets but also may discover some new properties of it. In this pa
【机 构】
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School of Computer Science and Engineering,University of Electronic Sinceand Technology of China,Che
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To study with other mathematical theories is an important research direction of rough sets. And this not only enrich the study of rough sets but also may discover some new properties of it. In this paper, we will study the rough set theory with the help of matroid theory. Firstly, each equivalence class of a partition is converted to a uniform matroid. Therefore, a partition is transformed into a set of uniform matroids. Secondly, the set of uniform matroids is combined through the operation of direct sum. And then a new matroid is obtained which can help us consider the set of uniform matroids as a whole. Furthermore, any subset of the universe is converted to a restriction matroid. Then the lower and upper approximations of the subset are established with the matroidal approach.For any two subsets of the universe, the relationship between the lower/upper approximations of them are discussed and some new properties are found. Finally,without the help of the lower and upper approximations, the boundary region and negative region of a subset of the universe are established with matroidal approach. And then the lower and upper approximations of the subset is obtained via the boundary region of the subset. This change the traditional idea in rough sets that the boundary region and negative region are obtained on the basis of the lower and upper approximations.
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