Covering-Based Rough Sets on Covering-Circuit Matroids
Rough set theory has been proposed by Pawlak as a useful and powerful tool for dealing with uncertainty,granularity,and incompleteness of knowledge in information systems.Matroid theory is a branch of combinatorial mathematics and widely used in optimization.Therefore,it is a good idea to integrate rough sets with matroids.In this paper,four types of covering approximation operators and their relationships are studied from the viewpoint of matroids.First,we define a new type of matroids named covering-circuit matroids whose all circuits form a covering.Second,for a covering-circuit matroid,we study the properties of the circuits of it from the perspective of coverings.Third,four types of covering approximation operators are represented by the circuits of the covering-circuit matroids.Moreover,we also investigate the relationships among four covering upper approximation operators.Finally,the conditions under which every type of covering upper approximation operator is the closure operator of the matroid are revealed.These results show many potential connections between covering-based rough sets and matroids.
Lab of Granular Computing Minnan Normal University,Zhangzhou 363000,China
The 2014 10th International Conference on Natural Computation (ICNC 2014) and the 2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2014)(第十届自然计算和第十一届模糊系统与知识发现国际会议)论文集
The 2014 10th International Conference on Natural Computation (ICNC 2014) and the 2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2014)(第十届自然计算和第十一届模糊系统与知识发现国际会议)