保持二元关系不变的概念约简

doi:10.16451/j.cnki.issn1003-6059.201806004

Abstract
Figure/Table
References (16)
Related Citation (9)

Download: PDF (713 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract

Inspired by the ideas of factorization and attribute reduction, the concept reduction preserving binary relations is proposed. Firstly, the definition of concept reduction preserving binary relations is given and the judgment theorems of corresponding consistent sets and reduct are proposed. Secondly, according to the roles of formal concepts in the process of concept reduction preserving binary relations, formal concepts are classified into three types: core concepts, relative necessary concepts and unnecessary concepts. Finally, the characteristics of three types of concepts are discussed, and the related conclusions about three types of concepts are given from the perspective of binary relations and operators. The results in this paper provide a research basis for the further study in algorithm,application and deeper theoretical analysis.

Received: 02 March 2018

ZTFLH:	O 29
	TP 18

Fund:

Supported by National Natural Science Foundation of China(No.61772021,11371014)

About author:: (CAO Li, master student. Her research interests include formal concept analysis.)

(WEI Ling(Corresponding author), Ph.D., professor. Her research interests include formal concept analysis, rough set and three-way concept analysis.)(QI Jianjun, Ph.D., associate professor. His research interests include three-way concept analysis, formal concept analysis, three-way decision and granular computing.)

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	CAO Li
	WEI Ling
	QI Jianjun

Cite this article:

CAO Li,WEI Ling,QI Jianjun. Concept Reduction Preserving Binary Relations[J]. , 2018, 31(6): 516-524.

URL:

http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.201806004 OR http://manu46.magtech.com.cn/Jweb_prai/EN/Y2018/V31/I6/516

[1] GANTER B, WILLE R. Formal Concept Analysis: Mathematical Foundations. New York, USA: Springer-Verlag, 1999.
[2] WILLE R. Restructuring Lattice Theory: An Approach Based on Hie-rarchies of Concepts // RIVAL I. Ordered Sets. Dordrecht, The Netherlands: Reidel, 1982: 445-470.
[3] YAO Y Y. Concept Lattices in Rough Set Theory // Proc of the IEEE Annual Meeting of the Fuzzy Information. New York, USA: IEEE, 2004: 796-801.
[4] 张文修,魏玲,祁建军.概念格的属性约简理论与方法.中国科学(E辑), 2005, 35(6): 628-639.
(ZHANG W X, WEI L, QI J J. Attribute Reduction Theory and Approach to Concept Lattice. Science in China(Series E), 2005, 35(6): 628-639.)
[5] WANG X, ZHANG W X. Knowledge Reduction in Concept Lattices Based on Irreducible Elements. Transactions on Computational Science V(Special Issue on Cognitive Knowledge Representation), 2009, 5540: 128-142.
[6] WU W Z, LEUNG Y, MI J S. Granular Computing and Knowledge Reduction in Formal Contexts. IEEE Transactions on Knowledge and Data Engineering, 2009, 21(10): 1461-1474.
[7] 魏玲,祁建军,张文修.决策形式背景的概念格属性约简.中国科学(E辑), 2008, 38(2): 195-208.
(WEI L, QI J J, ZHANG W X. Attribute Reduction Theory of Concept Lattice Based on Decision Formal Contexts. Science in China(Series E), 2008, 38(2): 195-208.)
[8] 张清华,王国胤,刘显全.基于最大粒的规则获取算法.模式识别与人工智能, 2012, 25(3): 388-396.
(ZHANG Q H, WANG G Y, LIU X Q. Rule Acquisition Algorithm Based on Maximal Granule. Pattern Recognition and Artificial Inte-lligence, 2012, 25(3): 388-396.)
[9] LI J H, MEI C L, WANG J H, et al. Rule-Preserved Object Compression in Formal Decision Contexts Using Concept Lattices. Knowledge-Based Systems, 2014, 71: 435-445.
[10] 朱治春,魏玲.基于类背景的双向规则的获取.西北大学学报(自然科学版), 2015, 45(4): 517-524.
(ZHU Z C, WEI L. Two-Way Rules Acquisition Based on Class Contexts. Journal of Northwest University(Natural Science Edition), 2015, 45(4): 517-524.)
[11] 刘琳,魏玲,钱婷.决策形式背景中具有置信度的三支规则提取.山东大学学报(理学版), 2017, 52(2): 101-110.
(LIU L, WEI L, QIAN T. Three-Way Rules Extraction in Formal Decision Contexts with Confidence. Journal of Shandong University(Natural Science), 2017, 52(2): 101-110.)
[12] KEPRT A, SNÁšEL V. Binary Factor Analysis with Help of Formal Concepts[C/OL].[2018-02-10].http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.87.3737&rep1&type=pdf.
[13] BELOHLAVEK R, VYCHODIL V. On Boolean Factor Analysis with Formal Concept as Factors[J/OL].[2018-02-10].http://phoebe.inf.upol.cz/~havrlanl/articles/BeVy_Bfafcf.pdf.
[14] BELOHLAVEK R, VYCHODIL V. Discovery of Optimal Factors in Binary Data via a Novel Method of Matrix Decomposition. Journal of Computer and System Sciences, 2010, 76(1): 3-20.
[15] KIM K H. Boolean Matrix Theory and Applications. New York, USA: Marcel Dekker, 1982.
[16] GLODEANU C V. Triadic Factor Analysis[C/OL].[2018-02-10].http://ceur-ws.org/Vol-672/paper12.pdf.