Abstract: This paper constructs the transversal matroidal structure of covering-based rough sets. It establishes a close relationship between coverings and normal matroids, and indicates the change relationship between coverings and transversal matroids in the matroidal structure. On the other hand, it provides an approach to induce a covering from a matroid, specifically, studies the relationship between two inductions. Finally, it proves that a covering can be induced by the transversal matroid induced by the covering if and only if the covering coincides with a partition.

Key words: rough sets, covering, transversal matroid, normal matroid

摘要： 通过结合拟阵理论, 建立了覆盖粗糙集的横贯拟阵结构; 在此结构下, 建立了覆盖与正规拟阵间的联系, 揭示了覆盖变化与相应的横贯拟阵变化的关系; 进一步给出了由任一拟阵导出覆盖的方法, 且研究了该方法和覆盖产生横贯拟阵的方法之间的联系; 证明了一个论域上的覆盖可由它产生的横贯拟阵导出, 当且仅当此覆盖是划分。

关键词: 粗糙集, 覆盖, 横贯拟阵, 正规拟阵