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Quasi-polynomial functions over bounded distributive lattices

dc.contributor.authorMarichal, Jean-Luc
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-09-26T14:07:46Z
dc.date.available2012-09-26T14:07:46Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10232
dc.language.isoenen
dc.subjectDistributive latticeen
dc.subjectPolynomial functionen
dc.subjectQuasi-polynomial functionen
dc.subjectFunctional equationen
dc.subjectAggregation functionen
dc.subjectDiscrete Sugeno integralen
dc.subjectUtility functionen
dc.subject.ddc512en
dc.titleQuasi-polynomial functions over bounded distributive latticesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversite du Luxembourg;
dc.description.abstractenIn [6] the authors introduced the notion of quasi-polynomial function as being a mapping f : X n → X defined and valued on a bounded chain X and which can be factorized as f(x1xn)=p((x1)(xn)) , where p is a polynomial function (i.e., a combination of variables and constants using the chain operations and ) and is an order-preserving map. In the current paper we study this notion in the more general setting where the underlying domain and codomain sets are, possibly different, bounded distributive lattices, and where the inner function is not necessarily order-preserving. These functions appear naturally within the scope of decision making under uncertainty since, as shown in this paper, they subsume overall preference functionals associated with Sugeno integrals whose variables are transformed by a given utility function. To axiomatize the class of quasi-polynomial functions, we propose several generalizations of well-established properties in aggregation theory, as well as show that some of the characterizations given in [6] still hold in this general setting. Moreover, we investigate the so-called transformed polynomial functions (essentially, compositions of unary mappings with polynomial functions) and show that, under certain conditions, they reduce to quasi-polynomial functions.en
dc.relation.isversionofjnlnameAequationes Mathematicae
dc.relation.isversionofjnlvol80en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages319-334en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00010-010-0039-9en
dc.identifier.urlsitehttp://arxiv.org/abs/0909.3009en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAlgèbreen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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