计算机科学 ›› 2016, Vol. 43 ›› Issue (4): 206-209.doi: 10.11896/j.issn.1002-137X.2016.04.042

• 人工智能 • 上一篇    下一篇

多粒化的模糊粗糙集代数

孔庆钊,韦增欣   

  1. 华东理工大学理学院 上海200237;集美大学理学院 厦门361021,广西大学数学与信息学院 南宁530004
  • 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(11161003,6,61472463,4),福建省教育厅科技项目(JA15281)资助

Fuzzy Rough Set Algebra of Multi-granulation

KONG Qing-zhao and WEI Zeng-xin   

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

摘要: 众所周知,一个粗糙集代数是由一个集合代数加上一对近似算子构成的。首先利用公理化的方法探讨经典的多粒化模糊粗糙集代数系统,可知经典的多粒化模糊粗糙集代数没有很好的性质;其次,引入 具有最小(大)元的等价关系的定义,并给出了基于具有最小(大)元等价关系的多粒化模糊近似算子的概念,在此基础上讨论了模糊粗糙集代数的性质,并得到了诸多结果。

关键词: 多粒化,模糊粗糙集代数,具有最小(大)元的等价关系,近似算子

Abstract: It is well known that a rough set algebra is a set algebra with added dual pair of rough approximation operators.In this paper,on the one hand,we discussed the classical fuzzy rough set algebra of multi-granulation by axiomatic approach.It is shown that the classical fuzzy rough set algebra do not obsess good properties.On the other hand,we defined the concept of equivalence relations with minimum (maximum) element.Moreover,multi-granulation fuzzy appro-ximation operators based on equivalence relations with minimum (maximum) element were defined.We discussed the properties of the fuzzy rough set algebra based on equivalence relations with minimum (maximum) element and got many excellent results.

Key words: Multi-granulation,Fuzzy rough set algebra,Equivalence relation with minimum (maximum) element,Approximation operators

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