Three-Way Concept Acquisition and Attribute Characteristic Analysis Based on Pictorial Diagrams

doi:10.3778/j.issn.1673-9418.2104120

Journal of Frontiers of Computer Science and Technology ›› 2022, Vol. 16 ›› Issue (12): 2879-2889.DOI: 10.3778/j.issn.1673-9418.2104120

• Theory and Algorithm • Previous Articles Next Articles

Three-Way Concept Acquisition and Attribute Characteristic Analysis Based on Pictorial Diagrams

WAN Qing¹^,²^,⁺(), MA Yingcang¹, LI Jinhai³^,⁴

1. School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xi’an 710127, China
3. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
4. Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, China

Received:2021-05-08 Revised:2021-06-29 Online:2022-12-01 Published:2021-06-23
About author:WAN Qing, born in 1986, Ph.D. candidate, associate professor. Her research interests include rough set theory, formal concept analysis, granular computing, etc.
MA Yingcang, born in 1972, Ph.D. candidate, professor. His research interests include rough set theory, machine learning, intelligent computing, etc.
LI Jinhai, born in 1984, Ph.D. candidate, professor. His research interests include concept-cognitive learning, granular computing, rough set theory, etc.
Supported by:
National Natural Science Foundation of China(12101478);National Natural Science Foundation of China(61772021);National Natural Science Foundation of China(61976130);Scientific Research Program Funded by Shaanxi Provincial Education Department(19JK0380)

基于直观图的三支概念获取及属性特征分析

万青¹^,²^,⁺(), 马盈仓¹, 李金海³^,⁴

1.西安工程大学理学院，西安 710048
2.西北大学概念、认知与智能研究中心，西安 710127
3.昆明理工大学理学院，昆明 650500
4.昆明理工大学数据科学研究中心，昆明 650500

通讯作者: +E-mail: wqysbe@163.com
作者简介:万青（1986—），女，陕西西安人，博士研究生，副教授，主要研究方向为粗糙集、形式概念分析、粒计算等。
马盈仓（1972—），男，陕西西安人，博士研究生，教授，主要研究方向为粗糙集、机器学习、智能计算等。
李金海（1984—），男，江西广丰人，博士研究生，教授，主要研究方向为概念认知学习、粒计算、粗糙集等。
基金资助:
国家自然科学基金(12101478);国家自然科学基金(61772021);国家自然科学基金(61976130);陕西省教育厅专项基金(19JK0380)

Abstract

Abstract:

Three-way concepts analysis, an effective tool for knowledge discovery, is a combination of three-way decision and formal concept analysis. Based on the connections between three-way concepts and formal concepts, the method of obtaining three-way concepts and the method of how to judge attribute characteristics are studied respectively from the perspective of pictorial diagrams. Inspired by the pictorial-diagrams-based acquisition methods of concepts (formal concept, object-oriented concept and property-oriented concept), and combining the connections between three kinds of concepts in combinatorial contexts and four kinds of three-way concepts, the definitions of combinatorial-property (combinatorial-object) pictorial diagram and property pair induced (object pair induced) three-way pictorial diagram are proposed. Then, the acquisition approaches to four kinds of three-way concepts are investigated by using the novel proposed pictorial diagrams. In addition, from the perspective of preserving the structure of the lattice, the general definitions of the reduction and attribute characteristics are given, attribute characteristics of an object induced three-way concept lattice are analyzed by discernibility matrix, and the judg-ment theorems of attribute characteristics are given based on property pair induced pictorial diagrams.

Key words: three-way concept, attribute characteristic, discernibility matrix, combinatorial pictorial diagram, three-way pictorial diagram

摘要：

三支概念分析是三支决策与形式概念分析的结合产物，是知识发现的有效工具。基于三支概念与形式概念的关联性，从直观图的角度研究了三支概念的获取方法以及属性特征的判别方法。借鉴形式概念分析中基于直观图获取概念、面向对象概念和面向属性概念的方法，并结合四种三支概念与混合背景的三种概念之间的联系，提出属性（对象）混合直观图和属性对（对象对）诱导的三支直观图的定义，进而利用形式背景的这两类直观图对四种三支概念的获取方法进行了研究。此外，给出保持格结构不变的约简和属性特征的一般化定义，通过辨识矩阵分析了对象诱导的三支概念格的属性特征，并基于属性对诱导的三支直观图得到了保持该格结构不变的属性特征的判别方法。

关键词: 三支概念, 属性特征, 差别矩阵, 混合直观图, 三支直观图

CLC Number:

TP18

WAN Qing, MA Yingcang, LI Jinhai. Three-Way Concept Acquisition and Attribute Characteristic Analysis Based on Pictorial Diagrams[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(12): 2879-2889.

万青, 马盈仓, 李金海. 基于直观图的三支概念获取及属性特征分析[J]. 计算机科学与探索, 2022, 16(12): 2879-2889.

Figures/Tables 14

Table 1 Formal context K = ( G , M , I )

G	a	b	c	d	e
x₁	+	+	-	+	+
x₂	+	+	+	-	-
x₃	-	-	-	+	-
x₄	+	+	+	-	+

Fig.1 Object pictorial diagram

Fig.2 Property pictorial diagram

Table 2 Complementary context of table 1

G	a	b	c	d	e
x₁	-	-	+	-	-
x₂	-	-	-	+	+
x₃	+	+	+	-	+
x₄	-	-	-	+	-

Table 3 Type I-combinatorial context

G	a	b	c	d	e	$a -$	$b -$	$c -$	$d -$	$e -$
x₁	+	+	-	+	+	-	-	+	-	-
x₂	+	+	+	-	-	-	-	-	+	+
x₃	-	-	-	+	-	+	+	+	-	+
x₄	+	+	+	-	+	-	-	-	+	-

Table 3 Type I-combinatorial context

G	a	b	c	d	e	$a -$	$b -$	$c -$	$d -$	$e -$
x₁	+	+	-	+	+	-	-	+	-	-
x₂	+	+	+	-	-	-	-	-	+	+
x₃	-	-	-	+	-	+	+	+	-	+
x₄	+	+	+	-	+	-	-	-	+	-

Table 4 Type II-combinatorial context

G	a	b	c	d	e
x₁	+	+	-	+	+
x₂	+	+	+	-	-
x₃	-	-	-	+	-
x₄	+	+	+	-	+
$x - 1$	-	-	+	-	-
$x - 2$	-	-	-	+	+
$x - 3$	+	+	+	-	+
$x - 4$	-	-	-	+	-

Table 4 Type II-combinatorial context

G	a	b	c	d	e
x₁	+	+	-	+	+
x₂	+	+	+	-	-
x₃	-	-	-	+	-
x₄	+	+	+	-	+
$x - 1$	-	-	+	-	-
$x - 2$	-	-	-	+	+
$x - 3$	+	+	+	-	+
$x - 4$	-	-	-	+	-

Fig.3 OEL(K) of table 1

Fig.4 AEL(K) of table1

Fig.5 OEOL(K) of table 1

Fig.6 AEPL(K) of table 1

Fig.7 Combinatorial-property pictorial diagram

Fig.8 Property pair induced three-way pictorial diagram

Fig.9 Combinatorial-object pictorial diagram

Fig.10 Object pair induced three-way pictorial diagram

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Three-Way Concept Acquisition and Attribute Characteristic Analysis Based on Pictorial Diagrams

基于直观图的三支概念获取及属性特征分析

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