dc.contributor.author Marichal, Jean-Luc dc.contributor.author Couceiro, Miguel dc.date.accessioned 2012-09-26T14:07:46Z dc.date.available 2012-09-26T14:07:46Z dc.date.issued 2010 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/10232 dc.language.iso en en dc.subject Distributive lattice en dc.subject Polynomial function en dc.subject Quasi-polynomial function en dc.subject Functional equation en dc.subject Aggregation function en dc.subject Discrete Sugeno integral en dc.subject Utility function en dc.subject.ddc 512 en dc.title Quasi-polynomial functions over bounded distributive lattices en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Universite du Luxembourg; dc.description.abstracten In [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.isversionofjnlname Aequationes Mathematicae dc.relation.isversionofjnlvol 80 en dc.relation.isversionofjnlissue 3 en dc.relation.isversionofjnldate 2010 dc.relation.isversionofjnlpages 319-334 en dc.relation.isversionofdoi http://dx.doi.org/10.1007/s00010-010-0039-9 en dc.identifier.urlsite http://arxiv.org/abs/0909.3009 en dc.relation.isversionofjnlpublisher Springer en dc.subject.ddclabel Algèbre en dc.relation.forthcoming non en dc.relation.forthcomingprint non en
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