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J4 ›› 2010, Vol. 45 ›› Issue (9): 32-37.

• 第十届中国Rough集与软计算学术会议专栏 • 上一篇    下一篇

中介公理集合论框架下的粗糙集

张闵敏1,曹丽霞2   

  1. 1.北京大学哲学系, 北京 100871; 261741部队, 北京 100081
  • 收稿日期:2010-06-13 出版日期:2010-09-16 发布日期:2010-10-12
  • 作者简介:张闵敏(1979-),女,助理研究员,博士,主要研究方向为人工智能和计算机科学中的逻辑等. Email:mimi-tml@126.com

The Rough set in the frame of the system of medium axiomatic set theory

ZHANG Min-min1, CAO Li-xia2   

  1. 1. Department of Philosophy, Peking University, Beijing 100871, China;
    2. 61741 Troops, Beijing 100081, China
  • Received:2010-06-13 Online:2010-09-16 Published:2010-10-12

摘要:

利用中介公理集合论来讨论粗糙集。首先给出中介化算子的公理化定义,讨论它的一些重要性质;其次给出与等价关系相对应的中介化算子的构造性定义,并指出它满足上述公理;再由中介化算子出发,构造出相应的等价关系。最后讨论中介化算子与等价关系之间的联系,证明两者是相互惟一确定的,用等价关系将集合改造成粗糙集与用相应的中介化算子将集合化为中介集,这两者是等效的。本文将粗糙集纳入中介公理系统理论框架之下,为研究粗糙集奠定了坚实的数学理论基础。

关键词: 粗糙集;中介公理集合论;等价关系;中介化算子

Abstract:

The Rough set is studied using the medium set theory as a new tool. Firstly, some of its important properties of the standard medium operator are discussed; then the definition of medium operator with the corresponding equivalence relation is given, and it is shown that it satisfies the axiom. Considering the medium operator starting, the corresponding equivalence relations are constructed. Finally, it is proved that intermediary between the operator and equivalence are the only identified each other. The equivalence relations are transformed into a collection of Rough sets and the appropriate mediumiary operator will set into a medium set,which are equivalent. Rough set is brought into the framework of the medium theory axiom system, which lay a solid mathematical foundation for the Rough set.

Key words: Rough set; medium set theory; medium operator; equivalent relation

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