2012/09/25 by Jingqian Wang, Wang, Jingqian, William Zhu +1
Computer Science · #Artificial Intelligence (cs.AI) #Data Mining Algorithms and Applications #FOS: Computer and information sciences #I.2.3 #I.2.4 #Image Processing and 3D Reconstruction #Rough Sets and Fuzzy Logic #cs.AI
paper · pdf · doi:10.48550/arxiv.1209.5482
11 pages
arxiv created 2012/09/25 · openalex publication_date 2012/09/25 · arxiv updated 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.