决策形式背景基于OE-协调性的属性约简

常丽娜; 魏玲; 彭超林

doi:10.16152/j.cnki.xdxbzr.2024-02-005

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决策形式背景基于OE-协调性的属性约简

粒计算与概念知识获取 | 更新时间：2024-04-19

- 决策形式背景基于OE-协调性的属性约简
- Attribute reduction in formal decision contexts based on OE-consistency
- 西北大学学报（自然科学版） 2024年54卷第2期页码：188-196
- 作者机构：
  
  1.长治学院　数学系，山西　长治　046011
  2.西北大学　概念、认知与智能研究中心，陕西　西安　710127
  3.西北大学　数学学院，陕西　西安　710127
  4.格拉斯哥大学　亚当斯密商学院，苏格兰　格拉斯哥　G128QQ
- 作者简介：
  
  常丽娜，女，副教授，从事形式概念分析、三支决策、博弈论等研究，bingdianlina@163.com。
  魏玲，女，教授，博士生导师，从事形式概念分析、三支决策、粒计算等研究，wl@nwu.edu.cn。
- 基金信息：
  
  国家自然科学基金(12171392);长治学院科研项目(XJZZ2021013)
- DOI：10.16152/j.cnki.xdxbzr.2024-02-005
  中图分类号： O29; TP18
- 纸质出版日期：2024-04-25，
  
  收稿日期：2023-08-30，
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常丽娜, 魏玲, 彭超林. 决策形式背景基于OE-协调性的属性约简[J]. 西北大学学报（自然科学版）, 2024,54(2):188-196.

CHANG Lina, WEI Ling, PENG Chaolin. Attribute reduction in formal decision contexts based on OE-consistency[J]. Journal of Northwest University (Natural Science Edition), 2024,54(2):188-196.
常丽娜, 魏玲, 彭超林. 决策形式背景基于OE-协调性的属性约简[J]. 西北大学学报（自然科学版）, 2024,54(2):188-196. DOI： 10.16152/j.cnki.xdxbzr.2024-02-005.

CHANG Lina, WEI Ling, PENG Chaolin. Attribute reduction in formal decision contexts based on OE-consistency[J]. Journal of Northwest University (Natural Science Edition), 2024,54(2):188-196. DOI： 10.16152/j.cnki.xdxbzr.2024-02-005.

摘要

属性约简作为形式概念分析中非常重要的一个研究分支，在三支概念分析中也同样重要。基于对象导出三支概念格，提出了保持决策形式背景OE-协调性的属性约简理论，丰富了三支概念分析的约简理论。首先，定义了决策形式背景的OE-协调集和OE-约简，并将属性按其特征分为3类。其次，指出OE-约简的本质就是极小OE-协调集，给出了OE-协调集的几个判定定理，通过研究OE-协调集的充要条件，获取OE-约简的判定定理。最后，给出OE-差别矩阵和OE-差别函数的定义，并给出了利用OE-差别矩阵和OE-差别函数计算OE-约简的方法。

Abstract

Attribute reduction

as a very important branch of formal concept analysis

is equally important in the three-way concept analysis. Based on object-induced concept lattices

attribute reduction theory which preserve OE-consistency of formal decision contexts is proposed

which enriches the reduction theory of three-way concept analysis. Firstly

OE-consistent set and OE-reduct of formal decision contexts are defined

and the attributes are classified into three categories according to their characteristics. Then

it is pointed out the essence of OE-reduct is minimal OE-consistent set

and several judgement theorems of OE-consistent set are given. By studying the necessary and sufficient conditions of OE-consistent set

judgement theorem of OE-reduct is obtained. Finally

the definition of OE-discernibility matrix and OE-discernibility function are given

and the method of calculating OE-reduct by using OE-discernibility matrix and OE-discernibility function is given.

关键词

三支概念分析属性约简OE-协调性决策形式背景对象导出三支概念格

Keywords

three-way concept analysisattribute reductionOE-consistencyformal decision contextsobject-induced three-way concept lattices

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