dc.contributor.author Waldhauser, Tamás dc.contributor.author Rico, Agnés dc.contributor.author Prade, Henri dc.contributor.author Dubois, Didier dc.contributor.author Couceiro, Miguel dc.date.accessioned 2012-10-02T12:50:05Z dc.date.available 2012-10-02T12:50:05Z dc.date.issued 2012 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/10418 dc.language.iso en en dc.subject Distributive lattice en dc.subject polynomial function en dc.subject interpolation en dc.subject.ddc 512 en dc.title General interpolation by polynomial functions of distributive lattices en dc.type Communication / Conférence dc.contributor.editoruniversityother University of Szeged; dc.contributor.editoruniversityother Universite Lyon I; dc.contributor.editoruniversityother IRIT; dc.contributor.editoruniversityother IRIT; dc.description.abstracten 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. en 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. dc.identifier.citationpages 347-355 en dc.relation.ispartofseriestitle Communications in Computer and Information Science en dc.relation.ispartofseriesnumber vol 299 en dc.relation.ispartoftitle 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 en dc.relation.ispartofeditor Greco, Salvatore dc.relation.ispartofeditor Bouchon-Meunier, Bernadette dc.relation.ispartofeditor Coletti, Giulianella dc.relation.ispartofeditor Fedrizzi, Mario dc.relation.ispartofeditor Matarazzo, Benedetto dc.relation.ispartofeditor Yager, Ronald R. dc.relation.ispartofpublname Springer en dc.relation.ispartofpublcity Berlin en dc.relation.ispartofdate 2012 dc.relation.ispartofpages 630 en dc.relation.ispartofurl http://dx.doi.org/10.1007/978-3-642-31718-7 en dc.subject.ddclabel Algèbre en dc.relation.ispartofisbn 978-3-642-31717-0 en dc.relation.conftitle 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU2012) en dc.relation.confdate 2012-07 dc.relation.confcity Catane en dc.relation.confcountry Italie en dc.relation.forthcoming non en dc.identifier.doi http://dx.doi.org/10.1007/978-3-642-31718-7_36 en
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