Computer Engineering and Applications ›› 2019, Vol. 55 ›› Issue (6): 50-56.DOI: 10.3778/j.issn.1002-8331.1805-0092

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Matroidal Structure Based on Set-Valued Mapping and Its Relationship with Covering Rough Sets

QI Meilan, LI Xiaonan   

  1. School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
  • Online:2019-03-15 Published:2019-03-14



  1. 西安电子科技大学 数学与统计学院,西安 710126

Abstract: In the topology theory, set-valued mapping is an important concept. According to the relationship of elements, a new type of matroidal structure is obtained due to set-valued mappings. Under this structure, some characteristics of this kind of matroid are investigated, such as independent sets, dependent sets, circuits, rank functions, closures and closed sets. At the same time, some equivalent characteristics of dual matroid with respect to this type of matroid are proposed, such as independent sets and circuits. In addition, based on the concept of neighborhood and approximation operator under the covering, the relationship between matroidal structure induced by set-valued mapping and rough set is established.

Key words: rough sets, covering, neighborhood, approximation, matroid

摘要: 集值映射是拓扑学中的一个重要的概念。基于论域中的各个元素之间的关系,利用集值映射的原理在论域上导出了一种拟阵结构,对该类拟阵的独立集、相关集、极小圈、秩函数、闭包和闭集等性质进行了研究,给出了该类拟阵的对偶拟阵的独立集和极小圈的等价刻画。利用覆盖粗糙集模型中邻域和近似算子的概念建立了集值映射下的拟阵结构和粗糙集之间的联系。

关键词: 粗糙集, 覆盖, 邻域, 近似算子, 拟阵