The Feature Description of Formal Context Based on the Relationships among Concept Lattices

Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the pap...

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Autores principales:	Ting Qian, Yongwei Yang, Xiaoli He
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	formal context concept lattice the three-way decision the three-way object oriented concept lattice II-dual intersectable context Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/c9f640610b3441df87a8ae7642b20dde
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id	oai:doaj.org-article:c9f640610b3441df87a8ae7642b20dde
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spelling	oai:doaj.org-article:c9f640610b3441df87a8ae7642b20dde2021-11-25T17:29:17ZThe Feature Description of Formal Context Based on the Relationships among Concept Lattices10.3390/e231113971099-4300https://doaj.org/article/c9f640610b3441df87a8ae7642b20dde2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1397https://doaj.org/toc/1099-4300Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.Ting QianYongwei YangXiaoli HeMDPI AGarticleformal contextconcept latticethe three-way decisionthe three-way object oriented concept latticeII-dual intersectable contextScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1397, p 1397 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	formal context concept lattice the three-way decision the three-way object oriented concept lattice II-dual intersectable context Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	formal context concept lattice the three-way decision the three-way object oriented concept lattice II-dual intersectable context Science Q Astrophysics QB460-466 Physics QC1-999 Ting Qian Yongwei Yang Xiaoli He The Feature Description of Formal Context Based on the Relationships among Concept Lattices
description	Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.
format	article
author	Ting Qian Yongwei Yang Xiaoli He
author_facet	Ting Qian Yongwei Yang Xiaoli He
author_sort	Ting Qian
title	The Feature Description of Formal Context Based on the Relationships among Concept Lattices
title_short	The Feature Description of Formal Context Based on the Relationships among Concept Lattices
title_full	The Feature Description of Formal Context Based on the Relationships among Concept Lattices
title_fullStr	The Feature Description of Formal Context Based on the Relationships among Concept Lattices
title_full_unstemmed	The Feature Description of Formal Context Based on the Relationships among Concept Lattices
title_sort	feature description of formal context based on the relationships among concept lattices
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c9f640610b3441df87a8ae7642b20dde
work_keys_str_mv	AT tingqian thefeaturedescriptionofformalcontextbasedontherelationshipsamongconceptlattices AT yongweiyang thefeaturedescriptionofformalcontextbasedontherelationshipsamongconceptlattices AT xiaolihe thefeaturedescriptionofformalcontextbasedontherelationshipsamongconceptlattices AT tingqian featuredescriptionofformalcontextbasedontherelationshipsamongconceptlattices AT yongweiyang featuredescriptionofformalcontextbasedontherelationshipsamongconceptlattices AT xiaolihe featuredescriptionofformalcontextbasedontherelationshipsamongconceptlattices
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The Feature Description of Formal Context Based on the Relationships among Concept Lattices

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