纯粹数学与应用数学2024,Vol.40Issue(1) :77-89.DOI:10.3969/j.issn.1008-5513.2024.01.006

不完备形式背景的三支近似概念约简

The three-way approximate concept reduction of incomplete formal contexts

任睿思 魏玲 李金海
纯粹数学与应用数学2024,Vol.40Issue(1) :77-89.DOI:10.3969/j.issn.1008-5513.2024.01.006

不完备形式背景的三支近似概念约简

The three-way approximate concept reduction of incomplete formal contexts

任睿思 1魏玲 1李金海2
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作者信息

  • 1. 西北大学数学学院,陕西西安 710071;西北大学概念,认知与智能研究中心,陕西 西安 710127
  • 2. 昆明理工大学数据科学研究中心,云南 昆明 650500
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摘要

不完备形式背景是形式概念分析中常见的数据表现形式,它可以反映对象和属性间的"具有","不具有"和"不确定是否具有"三种不同关系.本文在概念约简的框架下,从对象三支近似概念和属性三支近似概念两个角度出发,提出了不完备形式背景的三支近似概念约简理论;进一步通过定义三支近似代表概念矩阵以及三支近似代表概念函数,给出了求解不完备形式背景所有三支近似概念约简的方法.

Abstract

The incomplete formal context is commonly used in formal concept analysis to show in-complete date.It can reflect three different relationships between object and attribute:"possessing","not possessing"and"not sure whether the object possessing the attribute".Under the framework of concept reduction,this paper proposes the three-way approximate concept reduction theory of in-complete formal context from the perspectives of object-induced three-way approximate concepts and attribute-induced three-way approximate concepts.Furthermore,by introducing the three-way approx-imate representative concept matrix and the three-way approximate representative concept functions,a method for calculating all of the three-way approximate concept reducts of an incomplete formal context is provided.

关键词

不完备形式背景/三支近似概念/概念约简/代表概念矩阵

Key words

incomplete formal context/three-way approximate concept/concept reduction/representative concept matrix

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基金项目

国家自然科学基金(62006190)

国家自然科学基金(12171392)

出版年

2024
纯粹数学与应用数学
西北大学

纯粹数学与应用数学

影响因子:0.233
ISSN:1008-5513
参考文献量20
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