一种覆盖粗糙集的拟阵结构

南京大学学报(自然科学版) ›› 2013, Vol. 49 ›› Issue (5): 561–566.

一种覆盖粗糙集的拟阵结构

苏礼润，林姿琼，祝峰

出版日期:2014-01-21 发布日期:2014-01-21
作者简介:(闽南师范大学粒计算及其应用重点实验室,漳州,363000)
基金资助:
国家自然科学基金面上项目（61170128），福建省自然科学基金（2012J01294），福建省自然科学基金省属高校专项（JK2012028），福建省教育厅科技项目（JA12222），福建省计算机应用技术和信号与信息系统研究生教育创新基地（闽高教[2008]114 号）

A type of matroidal structure of covering-based rough sets

S Li-Run, Lin Zi-Qiong, Zhu William

Online:2014-01-21 Published:2014-01-21
About author:(Laboratory of Granular Computing, Minnan Normal University, Zhangzhou, 363000, China)

摘要/Abstract

摘要： 拟阵是一种图和矩阵的同时推广的概念，而覆盖粗糙集是经典粗糙集的推广。广义粗糙集与拟阵的结合已被广泛研究。通过结合拟阵中的基公理和覆盖中的友元，一方面，用友元构造出一个集族并且证明其满足拟阵的独立集公理，从而建立了一种覆盖的拟阵结构且介绍了一种拟阵即友元拟阵另一方面，在此结构下，讨论了拟阵的相关集极小圈秩函数闭包等表达形式，进一步还讨论了由不同覆盖能导出相同覆盖的条件以及由覆盖导出拟阵的闭包和覆盖上近似的关系。

Abstract: Matroids is an extension to graph and matrix, while covering rough set is a generalization of finite rough sets. The relationship between matroids and generalized rough sets based on relations has been studied from the viewpoint of linear independence of matrices. This paper constructs a matroidal structure of covering-based rough sets, which establishes a close relationship between coverings and matroids. On the one hand, a family of sets is constructed through indiscernible neighborhood in covering-based rough sets, and the family of sets is proved to satisfy independent sets axioms; in other word, a type of matroid, namely friends matroid, is induced. On the other hand, some characteristics of friends matroid, such as dependent sets, circuits, rank functions, are investigated with rough set approaches. Moreover, the relationship between the upper approximation operator of a set and its closure operator is investigated

苏礼润，林姿琼，祝峰. 一种覆盖粗糙集的拟阵结构[J]. 南京大学学报(自然科学版), 2013, 49(5): 561–566.

S Li-Run, Lin Zi-Qiong, Zhu William. A type of matroidal structure of covering-based rough sets[J]. Journal of Nanjing University(Natural Sciences), 2013, 49(5): 561–566.

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