Possibility theory and formal concept analysis in information systems

Dubois, D; Prade, H

Possibility theory and formal concept analysis in information systems

Dubois, D Prade, H

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Publication Type:: Conference Proceeding
Citation:: 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings, 2009, pp. 1021 - 1026
Issue Date:: 2009-12-01

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Field	Value	Language
dc.contributor.author	Dubois, D	en_US
dc.contributor.author	Prade, H https://orcid.org/0000-0003-4586-8527	en_US
dc.date.issued	2009-12-01	en_US
dc.identifier.citation	2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings, 2009, pp. 1021 - 1026	en_US
dc.identifier.isbn	9789899507968	en_US
dc.identifier.uri	http://hdl.handle.net/10453/32895
dc.description.abstract	The setting of formal concept analysis presupposes the existence of a relation between objects and properties. Knowing that an unspecified object has a given property induces a formal possibility distribution that models the set of objects known to possess this property. This view expressed in a recent work by the authors of the present paper, has led to introduce the set-valued counterpart to the four set functions evaluating potential or actual, possibility or necessity that underlie bipolar possibility theory, and to study associated notions. This framework puts formal concept analysis in a new, enlarged perspective, further explored in this article. The "actual (or guaranteed) possibility" function induces the usual Galois connexion that defines the notion of a concept as the pair of its extent and its intent. A new Galois connexion, based on the necessity measure, partitions the relation in "orthogonal" subsets of objects having distinct properties. Besides, the formal similarity between the notion of division in relational algebra and the "actual possibility" function leads to define the fuzzy set of objects having most properties in a set, and other related notions induced by fuzzy extensions of division. Generally speaking, the possibilistic view of formal concept analysis still applies when properties are a matter of degree, as discussed in the paper. Lastly, cases where the object / property relation is incomplete due to missing information, or more generally pervaded with possibilistic uncertainty is also discussed.	en_US
dc.relation.ispartof	2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings	en_US
dc.title	Possibility theory and formal concept analysis in information systems	en_US
dc.type	Conference Proceeding
utslib.for	0801 Artificial Intelligence and Image Processing	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.publication-status	Published	en_US

Abstract:

The setting of formal concept analysis presupposes the existence of a relation between objects and properties. Knowing that an unspecified object has a given property induces a formal possibility distribution that models the set of objects known to possess this property. This view expressed in a recent work by the authors of the present paper, has led to introduce the set-valued counterpart to the four set functions evaluating potential or actual, possibility or necessity that underlie bipolar possibility theory, and to study associated notions. This framework puts formal concept analysis in a new, enlarged perspective, further explored in this article. The "actual (or guaranteed) possibility" function induces the usual Galois connexion that defines the notion of a concept as the pair of its extent and its intent. A new Galois connexion, based on the necessity measure, partitions the relation in "orthogonal" subsets of objects having distinct properties. Besides, the formal similarity between the notion of division in relational algebra and the "actual possibility" function leads to define the fuzzy set of objects having most properties in a set, and other related notions induced by fuzzy extensions of division. Generally speaking, the possibilistic view of formal concept analysis still applies when properties are a matter of degree, as discussed in the paper. Lastly, cases where the object / property relation is incomplete due to missing information, or more generally pervaded with possibilistic uncertainty is also discussed.

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http://hdl.handle.net/10453/32895