Show simple item record

Quasi-Lovasz extensions and their symmetric counterparts

dc.contributor.authorMarichal, Jean-Luc
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-10-02T13:00:42Z
dc.date.available2012-10-02T13:00:42Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10419
dc.language.isoenen
dc.subjectAggregation functionen
dc.subjectdiscrete Choquet integralen
dc.subjectLovász extensionen
dc.subjectfunctional equationen
dc.subjectcomonotonic modularityen
dc.subjectsymmetrizationen
dc.subject.ddc512en
dc.titleQuasi-Lovasz extensions and their symmetric counterpartsen
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherUniversite du Luxembourg;
dc.description.abstractenWe introduce the concept of quasi-Lovász extension as being a mapping f:InI\!R defined over a nonempty real interval I containing the origin, and which can be factorized as f(x 1,…,x n ) = L(ϕ(x 1),…,ϕ(x n )), where L is the Lovász extension of a pseudo-Boolean function :01nI\!R (i.e., the function L:I\!RnI\!R whose restriction to each simplex of the standard triangulation of [0,1] n is the unique affine function which agrees with ψ at the vertices of this simplex) and :II\!R is a nondecreasing function vanishing at the origin. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals whose variables are transformed by a given utility function. To axiomatize the class of quasi-Lovász extensions, we propose generalizations of properties used to characterize the Lovász extensions, including a comonotonic version of modularity and a natural relaxation of homogeneity. A variant of the latter property enables us to axiomatize also the class of symmetric quasi-Lovász extensions, which are compositions of symmetric Lovász extensions with 1-place nondecreasing odd functions.en
dc.identifier.citationpages178-187en
dc.relation.ispartofseriestitleCommunications in Computer and Information Scienceen
dc.relation.ispartofseriesnumbervol 300en
dc.relation.ispartoftitleAdvances in Computational Intelligence. 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IVen
dc.relation.ispartofeditorGreco, Salvatore
dc.relation.ispartofeditorBouchon-Meunier, Bernadette
dc.relation.ispartofeditorColetti, Giulianella
dc.relation.ispartofeditorFedrizzi, Mario
dc.relation.ispartofeditorMatarazzo, Benedetto
dc.relation.ispartofeditorYager, Ronald R.
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlinen
dc.relation.ispartofdate2012
dc.relation.ispartofpages710en
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-3-642-31724-8en
dc.subject.ddclabelAlgèbreen
dc.relation.ispartofisbn978-3-642-31723-1en
dc.relation.conftitle14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU2012)en
dc.relation.confdate2012-07
dc.relation.confcityCataneen
dc.relation.confcountryItalieen
dc.relation.forthcomingnonen
dc.identifier.doihttp://dx.doi.org/10.1007/978-3-642-31724-8_19en


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record