计算机科学 ›› 2016, Vol. 43 ›› Issue (1): 57-60.doi: 10.11896/j.issn.1002-137X.2016.01.013

• CRSSC-CWI-CGrC2015 • 上一篇    下一篇

由邻域导出的拟阵结构

李卉,祝峰,林姿琼   

  1. 闽南师范大学福建省粒计算及其应用重点实验室 漳州363000,闽南师范大学福建省粒计算及其应用重点实验室 漳州363000,闽南师范大学福建省粒计算及其应用重点实验室 漳州363000
  • 出版日期:2018-12-01 发布日期:2018-12-01
  • 基金资助:
    本文受国家自然科学基金面上项目(61170128,61379049),福建省教育厅科技重点项目(JA13192),福建省教育厅项目(产学研项目)(JA14194),福建省科技计划重点项目(2012H0043)资助

Matroidal Structure Induced by Neighborhood

LI Hui, ZHU Feng and LIN Zi-qiong   

  • Online:2018-12-01 Published:2018-12-01

摘要: 通过利用覆盖的邻域和补邻域构造了一个集族,并且证明其满足拟阵的独立集公理,从而建立了一种拟阵结构,并且对这种拟阵的相关集、极小圈、秩函数和闭包等表达形式进行了研究。最后,给出了此类拟阵的对偶拟阵的独立集、极小圈的等价刻画。

关键词: 粗糙集,覆盖,邻域,补邻域,拟阵

Abstract: This paper constructed a matroidal structure by the neighborhood of a covering.At first,a family of sets was constructed through neighborhood and complementary neighborhood on a covering and the family of sets was proved to satisfy independent set axioms.Thus a matroidal structure of a covering was established.Then,we investigated some characteristics of this kind of matroid,such as dependent set,circuit,rank function and closure.At last,we gave some equivalent characterizations of dual matroid of the matroid,such as independent set and cicuit.

Key words: Rough set,Covering,Neighborhood,Complementary neighborhood,Matroid

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