The structure of oppositions in rough set theory and formal concept analysis - Toward a new bridge between the two settings

Ciucci, D; Dubois, D; Prade, H

The structure of oppositions in rough set theory and formal concept analysis - Toward a new bridge between the two settings

Ciucci, D Dubois, D Prade, H

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Publication Type:: Conference Proceeding
Citation:: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2014, 8367 LNCS pp. 154 - 173
Issue Date:: 2014-04-14

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Field	Value	Language
dc.contributor.author	Ciucci, D	en_US
dc.contributor.author	Dubois, D	en_US
dc.contributor.author	Prade, H https://orcid.org/0000-0003-4586-8527	en_US
dc.date.issued	2014-04-14	en_US
dc.identifier.citation	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2014, 8367 LNCS pp. 154 - 173	en_US
dc.identifier.isbn	9783319049380	en_US
dc.identifier.issn	0302-9743	en_US
dc.identifier.uri	http://hdl.handle.net/10453/120796
dc.description.abstract	Rough set theory (RST) and formal concept analysis (FCA) are two formal settings in information management, which have found applications in learning and in data mining. Both rely on a binary relation. FCA starts with a formal context, which is a relation linking a set of objects with their properties. Besides, a rough set is a pair of lower and upper approximations of a set of objects induced by an indistinguishability relation; in the simplest case, this relation expresses that two objects are indistinguishable because their known properties are exactly the same. It has been recently noticed, with different concerns, that any binary relation on a Cartesian product of two possibly equal sets induces a cube of oppositions, which extends the classical Aristotelian square of oppositions structure, and has remarkable properties. Indeed, a relation applied to a given subset gives birth to four subsets, and to their complements, that can be organized into a cube. These four subsets are nothing but the usual image of the subset by the relation, together with similar expressions where the subset and / or the relation are replaced by their complements. The eight subsets corresponding to the vertices of the cube can receive remarkable interpretations, both in the RST and the FCA settings. One facet of the cube corresponds to the core of RST, while basic FCA operators are found on another facet. The proposed approach both provides an extended view of RST and FCA, and suggests a unified view of both of them. © 2014 Springer International Publishing.	en_US
dc.relation.ispartof	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en_US
dc.relation.isbasedon	10.1007/978-3-319-04939-7_7	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	The structure of oppositions in rough set theory and formal concept analysis - Toward a new bridge between the two settings	en_US
dc.type	Conference Proceeding
utslib.citation.volume	8367 LNCS	en_US
utslib.for	0804 Data Format	en_US
utslib.for	0803 Computer Software	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Software
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US
pubs.volume	8367 LNCS	en_US

Abstract:

Rough set theory (RST) and formal concept analysis (FCA) are two formal settings in information management, which have found applications in learning and in data mining. Both rely on a binary relation. FCA starts with a formal context, which is a relation linking a set of objects with their properties. Besides, a rough set is a pair of lower and upper approximations of a set of objects induced by an indistinguishability relation; in the simplest case, this relation expresses that two objects are indistinguishable because their known properties are exactly the same. It has been recently noticed, with different concerns, that any binary relation on a Cartesian product of two possibly equal sets induces a cube of oppositions, which extends the classical Aristotelian square of oppositions structure, and has remarkable properties. Indeed, a relation applied to a given subset gives birth to four subsets, and to their complements, that can be organized into a cube. These four subsets are nothing but the usual image of the subset by the relation, together with similar expressions where the subset and / or the relation are replaced by their complements. The eight subsets corresponding to the vertices of the cube can receive remarkable interpretations, both in the RST and the FCA settings. One facet of the cube corresponds to the core of RST, while basic FCA operators are found on another facet. The proposed approach both provides an extended view of RST and FCA, and suggests a unified view of both of them. © 2014 Springer International Publishing.

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http://hdl.handle.net/10453/120796