Qualitative capacities as imprecise possibilities

Dubois, D; Prade, H; Rico, A

Qualitative capacities as imprecise possibilities

Dubois, D Prade, H

Rico, A

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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), 2013, 7958 LNAI pp. 169 - 180
Issue Date:: 2013-08-01

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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.contributor.author	Rico, A	en_US
dc.date.issued	2013-08-01	en_US
dc.identifier.citation	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2013, 7958 LNAI pp. 169 - 180	en_US
dc.identifier.isbn	9783642390906	en_US
dc.identifier.issn	0302-9743	en_US
dc.identifier.uri	http://hdl.handle.net/10453/32897
dc.description.abstract	This paper studies the structure of qualitative capacities, that is, monotonic set-functions, when they range on a finite totally ordered scale equipped with an order-reversing map. These set-functions correspond to general representations of uncertainty, as well as importance levels of groups of criteria in multicriteria decision-making. More specifically, we investigate the question whether these qualitative set-functions can be viewed as classes of simpler set-functions, typically possibility measures, paralleling the situation of quantitative capacities with respect to imprecise probability theory. We show that any capacity is characterized by a non-empty class of possibility measures having the structure of an upper semi-lattice. The lower bounds of this class are enough to reconstruct the capacity, and their number is characteristic of its complexity. We introduce a sequence of axioms generalizing the maxitivity property of possibility measures, and related to the number of possibility measures needed for this reconstruction. In the Boolean case, capacities are closely related to non-regular multi-source modal logics and their neighborhood semantics can be described in terms of qualitative Moebius transforms. © 2013 Springer-Verlag Berlin Heidelberg.	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	10.1007/978-3-642-39091-3-15	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Qualitative capacities as imprecise possibilities	en_US
dc.type	Conference Proceeding
utslib.citation.volume	7958 LNAI	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	closed_access
pubs.publication-status	Published	en_US
pubs.volume	7958 LNAI	en_US

Abstract:

This paper studies the structure of qualitative capacities, that is, monotonic set-functions, when they range on a finite totally ordered scale equipped with an order-reversing map. These set-functions correspond to general representations of uncertainty, as well as importance levels of groups of criteria in multicriteria decision-making. More specifically, we investigate the question whether these qualitative set-functions can be viewed as classes of simpler set-functions, typically possibility measures, paralleling the situation of quantitative capacities with respect to imprecise probability theory. We show that any capacity is characterized by a non-empty class of possibility measures having the structure of an upper semi-lattice. The lower bounds of this class are enough to reconstruct the capacity, and their number is characteristic of its complexity. We introduce a sequence of axioms generalizing the maxitivity property of possibility measures, and related to the number of possibility measures needed for this reconstruction. In the Boolean case, capacities are closely related to non-regular multi-source modal logics and their neighborhood semantics can be described in terms of qualitative Moebius transforms. © 2013 Springer-Verlag Berlin Heidelberg.

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http://hdl.handle.net/10453/32897