粗糙集与拟阵收缩
Rough sets and matroidal contraction
摘要：
粗糙集是数据采掘中数据预处理的有效方法。拟阵作为向量空间线性无关性的推广，为贪心算法提供了良好的平台。本文将粗糙集应用于拟阵，研究了拟阵对偶的压缩性。首先，对于论域上的等价关系，通过下近似算子建立粗糙集的拟阵结构。其次，研究了拟阵的对偶及其独立集、基、秩函数等性质。最后，研究了对偶拟阵到单点集的补的收缩与对偶拟阵到该点的等价类的补的收缩之间的关系。
英文摘要：
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
