Structures of opposition induced by relations: The Boolean and the gradual cases

Ciucci, D; Dubois, D; Prade, H

Structures of opposition induced by relations: The Boolean and the gradual cases

Ciucci, D Dubois, D Prade, H

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Publication Type:: Journal Article
Citation:: Annals of Mathematics and Artificial Intelligence, 2016, 76 (3-4), pp. 351 - 373
Issue Date:: 2016-04-01

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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	2016-04-01	en_US
dc.identifier.citation	Annals of Mathematics and Artificial Intelligence, 2016, 76 (3-4), pp. 351 - 373	en_US
dc.identifier.issn	1012-2443	en_US
dc.identifier.uri	http://hdl.handle.net/10453/118737
dc.description.abstract	© 2015, Springer International Publishing Switzerland. The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.	en_US
dc.relation.ispartof	Annals of Mathematics and Artificial Intelligence	en_US
dc.relation.isbasedon	10.1007/s10472-015-9480-8	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Structures of opposition induced by relations: The Boolean and the gradual cases	en_US
dc.type	Journal Article
utslib.citation.volume	3-4	en_US
utslib.citation.volume	76	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0802 Computation Theory and Mathematics	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	closed_access
pubs.issue	3-4	en_US
pubs.publication-status	Published	en_US
pubs.volume	76	en_US

Abstract:

© 2015, Springer International Publishing Switzerland. The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.

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http://hdl.handle.net/10453/118737