2013/11/05 by Bin Yang, Yang, Bin, William Zhu +1
Computer Science · #Artificial Intelligence (cs.AI) #Data Mining Algorithms and Applications #FOS: Computer and information sciences #Rough Sets and Fuzzy Logic #cs.AI
paper · pdf · doi:10.48550/arxiv.1311.0944
16 pages, 8figures
arxiv created 2013/11/05 · openalex publication_date 2013/11/05 · arxiv updated 2013/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems. The connectivity of a matroid is an important measure of its robustness as a network. Therefore, it is very necessary to investigate the conditions under which a matroid is connected. In this paper, the connectivity for matroids is studied through relation-based rough sets. First, a symmetric and transitive relation is introduced from a general matroid and its properties are explored from the viewpoint of matroids. Moreover, through the relation introduced by a general matroid, an undirected graph is generalized. Specifically, the connection of the graph can be investigated by the relation-based rough sets. Second, we study the connectivity for matroids by means of relation-based rough sets and some conditions under which a general matroid is connected are presented. Finally, it is easy to prove that the connectivity for a general matroid with some special properties and its induced undirected graph is equivalent. These results show an important application of relation-based rough sets to matroids.