General interpolation by polynomial functions of distributive lattices
Waldhauser, Tamás; Rico, Agnés; Prade, Henri; Dubois, Didier; Couceiro, Miguel (2012), General interpolation by polynomial functions of distributive lattices, dans Greco, Salvatore; Bouchon-Meunier, Bernadette; Coletti, Giulianella; Fedrizzi, Mario; Matarazzo, Benedetto; Yager, Ronald R., Advances 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 III, Springer : Berlin, p. 347-355. http://dx.doi.org/10.1007/978-3-642-31718-7_36
Type
Communication / ConférenceDate
2012Titre du colloque
14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU2012)Date du colloque
2012-07Ville du colloque
CatanePays du colloque
ItalieTitre de l'ouvrage
Advances 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 IIIAuteurs de l’ouvrage
Greco, Salvatore; Bouchon-Meunier, Bernadette; Coletti, Giulianella; Fedrizzi, Mario; Matarazzo, Benedetto; Yager, Ronald R.Éditeur
Springer
Titre de la collection
Communications in Computer and Information ScienceNuméro dans la collection
vol 299Ville d’édition
Berlin
Isbn
978-3-642-31717-0
Nombre de pages
630Pages
347-355
Identifiant publication
Métadonnées
Afficher la notice complèteRésumé (EN)
For a distributive lattice L, we consider the problem of interpolating functions f : D → L defined on a finite set D ⊆ L n , by means of lattice polynomial functions of L. Two instances of this problem have already been solved. In the case when L is a distributive lattice with least and greatest elements 0 and 1, Goodstein proved that a function f : {0,1} n → L can be interpolated by a lattice polynomial function p : L n → L if and only if f is monotone; in this case, the interpolating polynomial p was shown to be unique. The interpolation problem was also considered in the more general setting where L is a distributive lattice, not necessarily bounded, and where D ⊆ L n is allowed to range over cuboids D=a1,b1×⋯×an,bn with a i ,b i ∈ L and a i < b i . In this case, the class of such partial functions that can be interpolated by lattice polynomial functions was completely described. In this paper, we extend these results by completely characterizing the class of lattice functions that can be interpolated by polynomial functions on arbitrary finite subsets D ⊆ L n . As in the latter setting, interpolating polynomials are not necessarily unique. We provide explicit descriptions of all possible lattice polynomial functions that interpolate these lattice functions, when such an interpolation is available.Mots-clés
Distributive lattice; polynomial function; interpolationPublications associées
Affichage des éléments liés par titre et auteur.
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Waldhauser, Tamás; Couceiro, Miguel (2013) Article accepté pour publication ou publié
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Brabant, Quentin; Couceiro, Miguel; Dubois, Didier; Prade, Henri; Rico, Agnès (2018) Communication / Conférence
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Dubois, Didier; Prade, Henri; Waldhauser, Tamás; Couceiro, Miguel (2012) Communication / Conférence
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Waldhauser, Tamás; Couceiro, Miguel (2011) Communication / Conférence
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Waldhauser, Tamás; Couceiro, Miguel (2014) Article accepté pour publication ou publié