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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (1): 60-67.doi: 10.6040/j.issn.1671-9352.0.2020.205

• • 上一篇    

基于图的悲观多粒度粗糙集粒度约简

张文娟1,李进金1*,林艺东1,2   

  1. 1.闽南师范大学数学与统计学院, 福建 漳州 363000;2.厦门大学数学科学学院, 福建 厦门 361000
  • 发布日期:2021-01-05
  • 作者简介:张文娟(1995— ), 女, 硕士研究生, 研究方向为粗糙集和概念格. E-mail:z_wenjuan@126.com*通信作者简介:李进金(1960— ), 男, 博士, 教授, 博士生导师, 研究方向为拓扑学、粗糙集、概念格等. E-mail:jinjinli@mnnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11871259,11701258);福建省自然科学基金重点项目(2019J01748,2017J01507,2020J02043)

Graph-based granularity reduction in pessimistic multi-granulation rough set

ZHANG Wen-juan1, LI Jin-jin1*, LIN Yi-dong1,2   

  1. 1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China;
    2. School of Mathematical Sciences, Xiamen University, Xiamen 361000, Fujian, China
  • Published:2021-01-05

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摘要： 结合图的顶点覆盖理论,探讨了悲观多粒度粗糙集粒度约简的新方法。首先提出悲观多粒度粗糙集诱导图的概念, 并给出其粒度约简的图特征,在此基础上,以图的方法刻画粒度的重要度,进而设计基于图的悲观多粒度粗糙集粒度约简的算法;其次,定义悲观多粒度决策粗糙集诱导图的概念,类似地给出其粒度约简的图特征和粒度重要度,设计基于图的悲观多粒度决策粗糙集粒度约简的算法; 最后,利用实例说明悲观下近似多粒度粗糙集粒度约简算法的合理性。

关键词: 粒度约简, 图论, 多粒度粗糙集, 顶点覆盖

Abstract: This paper combines the theory of the vertex cover of graph, and a new method of the granularity reduction of pessimistic multi-granulation rough set is discussed. Firstly, the concept of the graph induced from pessimistic multi-granulation rough set is presented, and the graph characteristic of its granularity reduction is given. On this basis, the significance of granularity is depicted by the method of graph, and then a algorithm about granularity reduction of pessimistic multi-granulation rough set based on graph is designed. Secondly, the concept of the graph induced from multi-granulation decision-theoretic rough set is defined, the graph characteristic of its granularity reduction and the significance of granularity are proposed at the same way, then a algorithm of granularity reduction of pessimistic multi-granulation decision-theoretic rough set based on graph is designed. Finally, it is rational to give an example to illustrate the pessimistic lower approximate multi-granulation rough set algorithm.

Key words: granularity reduction, graph theory, multi-granulation rough set, vertex cover

中图分类号: 

  • TP18
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