Quasi-polynomial functions over bounded distributive lattices
Marichal, Jean-Luc; Couceiro, Miguel (2010), Quasi-polynomial functions over bounded distributive lattices, Aequationes Mathematicae, 80, 3, p. 319-334. http://dx.doi.org/10.1007/s00010-010-0039-9
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Article accepté pour publication ou publiéLien vers un document non conservé dans cette base
http://arxiv.org/abs/0909.3009Date
2010Nom de la revue
Aequationes MathematicaeVolume
80Numéro
3Éditeur
Springer
Pages
319-334
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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.Mots-clés
Distributive lattice; Polynomial function; Quasi-polynomial function; Functional equation; Aggregation function; Discrete Sugeno integral; Utility functionPublications associées
Affichage des éléments liés par titre et auteur.
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Marichal, Jean-Luc; Couceiro, Miguel (2012) Article accepté pour publication ou publié
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Marichal, Jean-Luc; Couceiro, Miguel (2011) Article accepté pour publication ou publié
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Marichal, Jean-Luc; Couceiro, Miguel (2009) Communication / Conférence
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Marichal, Jean-Luc; Couceiro, Miguel (2009) Article accepté pour publication ou publié
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Marichal, Jean-Luc; Couceiro, Miguel (2010) Article accepté pour publication ou publié