基于直观图的三支概念获取及属性特征分析

doi:10.3778/j.issn.1673-9418.2104120

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (12): 2879-2889.DOI: 10.3778/j.issn.1673-9418.2104120

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

收稿日期:2021-05-08 修回日期:2021-06-29 出版日期:2022-12-01 发布日期:2021-06-23
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)

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)

摘要/Abstract

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

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

中图分类号:

TP18

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.

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.

图/表 14

表1 形式背景 K = ( G , M , I )

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

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

图1 对象直观图

Fig.1 Object pictorial diagram

图2 属性直观图

Fig.2 Property pictorial diagram

表2 表1的补背景

Table 2 Complementary context of table 1

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

表3 I型混合背景

Table 3 Type I-combinatorial context

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

表3 I型混合背景

Table 3 Type I-combinatorial context

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

表4 II型混合背景

Table 4 Type II-combinatorial context

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

表4 II型混合背景

Table 4 Type II-combinatorial context

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

图3 表1的OEL(K)

Fig.3 OEL(K) of table 1

图4 表1的AEL(K)

Fig.4 AEL(K) of table1

图5 表1的OEOL(K)

Fig.5 OEOL(K) of table 1

图6 表1的AEPL(K)

Fig.6 AEPL(K) of table 1

图7 属性混合直观图

Fig.7 Combinatorial-property pictorial diagram

图8 属性对诱导的三支直观图

Fig.8 Property pair induced three-way pictorial diagram

图9 对象混合直观图

Fig.9 Combinatorial-object pictorial diagram

图10 对象对诱导的三支直观图

Fig.10 Object pair induced three-way pictorial diagram

参考文献 28

[1]	GANTER B, WILLE R. Formal concept analysis: mathema-tical foundations[M]. Berlin, Heidelberg: Springer, 1999.
[2]	PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Science, 1982, 11(5): 341-356. DOI URL
[3]	DÜNTSCH I, GEDIGA G. Modal-style operators in qualita-tive data analysis[C]// Proceedings of the 2002 IEEE Inter-national Conference on Data Mining, Maebashi City, Dec 9-12, 2002. Washington: IEEE Computer Society, 2002: 155-162.
[4]	YAO Y Y. A comparative study of formal concept analysis and rough set theory in data analysis[C]// LNCS 3066: Pro-ceedings of the 4th International Conference on Rough Sets and Current Trends in Computing, Uppsala, Jun 1-5, 2004.Berlin, Heidelberg: Springer, 2004: 59-68.
[5]	YAO Y Y. Three-way decision: an interpretation of rules in rough set theory[C]// Proceedings of the 4th International Conference on Rough Sets and Knowledge Technology, Gold Coast, Jul 14-16, 2009. Cham: Springer, 2009: 642-649.
[6]	QI J J, WEI L, YAO Y Y. Three-way formal concept analysis[C]// LNCS 8818: Proceedings of the 9th International Con-ference on Rough Sets and Knowledge Technology, Shang-hai, Oct 24-26, 2014. Cham: Springer, 2014: 732-741.
[7]	QI J J, QIAN T, WEI L. The connections between three-way and classical lattices[J]. Knowledge-Based Systems, 2016, 91: 143-151. DOI URL
[8]	QIAN T, WEI L, QI J J. Constructing three-way concept la-ttices based on apposition and subposition of formal contexts[J]. Knowledge-Based Systems, 2017, 116: 39-48. DOI URL
[9]	WEI L, QIAN T. The three-way object oriented concept lat-tice and the three-way property oriented concept lattice[C]// Proceedings of the 2015 International conference on Ma-chine Learning and Cybernetics, Guangzhou, Jul 12-15, 2015. Piscataway: IEEE, 2015: 854-859.
[10]	QIAN T, WEI L, QI J J. A theoretical study on the object (property) oriented concept lattices based on three-way deci-sions[J]. Soft Computing, 2019, 23(19): 9477-9489. DOI URL
[11]	YU H Y, LI Q G, CAI M J. Characteristics of three-way concept lattices and three-way rough concept lattices[J]. Knowledge-Based Systems, 2018, 146: 181-189. DOI URL
[12]	YAO Y Y. Interval sets and three-way concept analysis in incomplete contexts[J]. International Journal of Machine Lear-ning and Cybernetics, 2017, 8(1): 3-20.
[13]	LI M Z, WANG G Y. Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts[J]. Knowledge-Based Systems, 2016, 91: 165-178. DOI URL
[14]	REN R S, WEI L. The attribute reductions of three-way con-cept lattices[J]. Knowledge-Based Systems, 2016, 99: 92-102. DOI URL
[15]	李美争, 王国胤. 三支近似概念格中基于对象-概念辨识矩阵的属性约简方法[J]. 控制与决策, 2016, 31(10): 1779-1784.
	LI M Z, WANG G Y. Object-concept discernibility matrix based approach to attribute reduction in three-way appro-ximate concept lattice[J]. Control and Decision, 2016, 31(10): 1779-1784.
[16]	WEI L, LIU L, QI J J, et al. Rules acquisition of formal decision contexts based on three-way concept lattices[J]. Information Sciences, 2020, 516: 529-544. DOI URL
[17]	任睿思, 魏玲, 祁建军. 三支弱协调决策形式背景的规则获取[J]. 山东大学学报(理学版), 2018, 53(6): 76-85.
	REN R S, WEI L, QI J J. Rules acquisition on three-way weakly consistent formal decision contexts[J]. Journal of Shan-dong University (Natural Science), 2018, 53(6): 76-85.
[18]	LI J H, HUANG C C, QI J J, et al. Three-way cognitive con-cept learning via multi-granularity[J]. Information Sciences, 2017, 378 (1): 244-263. DOI URL
[19]	HUANG C C, LI J H, MEI C L, et al. Three-way concept learning based on cognitive operators: an information fusion viewpoint[J]. International Journal of Approximate Reasoning, 2017, 83: 218-242. DOI URL
[20]	徐伟华, 杨蕾, 张晓燕. 模糊三支形式概念分析与概念认知学习[J]. 西北大学学报(自然科学版), 2020, 50(4): 516-528.
	XU W H, YANG L, ZHANG X Y. Fuzzy three-way formal concept analysis and concept-cognitive learning[J]. Journal of Northwest University(Natural Science Edition), 2020, 50(4): 516-528.
[21]	龙柄翰, 徐伟华. 模糊三支概念分析与模糊三支概念格[J]. 南京大学学报(自然科学版), 2019, 55(4): 537-545.
	LONG B H, XU W H. Fuzzy three-way concept analysis and fuzzy three-way concept lattice[J]. Journal of Nanjing University(Natural Sciences), 2019, 55(4): 537-545.
[22]	姬儒雅, 魏玲, 任睿思, 等. 毕达哥拉斯模糊三支概念格[J]. 山东大学学报(理学版), 2020, 55(11): 58-65.
	JI R Y, WEI L, REN R S, et al. Pythagorean fuzzy three-way concept lattice[J]. Journal of Shandong University (Natural Science), 2020, 55(11): 58-65.
[23]	SINGH P K. Three-way fuzzy concept lattice representation using neutrosophic set[J]. International Journal of Machine Learning and Cybernetics, 2017, 8(1): 69-79. DOI URL
[24]	SINGH P K. Medical diagnoses using three-way fuzzy con-cept lattice and their Euclidean distance[J]. Computational and Applied Mathematics, 2018, 37 (3): 3283-3306. DOI URL
[25]	SHIVHARE R, CHERUKURI A K. Three-way conceptual approach for cognitive memory functionalities[J]. International Journal of Machine Learning and Cybernetics, 2017, 8(1): 21-34. DOI URL
[26]	CHEN X Y, QI J J, ZHU X, et al. Unlabelled text mining methods based on two extension models of concept lattices[J]. International Journal of Machine Learning and Cyberne-tics, 2020, 11: 475-490.
[27]	WEI L, WAN Q. Granular transformation and irreducible elements judgment based on pictorial diagrams[J]. IEEE Tran-sactions on Cybernetics, 2016, 46(2): 380-387.
[28]	WAN Q, WEI L. Attribute reduction based on property pic-torial diagram[J]. The Scientific World Journal, 2014: 109706.

基于直观图的三支概念获取及属性特征分析

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

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 14

参考文献 28

相关文章 1

编辑推荐

Metrics