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General interpolation by polynomial functions of distributive lattices

dc.contributor.authorWaldhauser, Tamás
dc.contributor.authorRico, Agnés
dc.contributor.authorPrade, Henri
HAL ID: 743299
ORCID: 0000-0003-4586-8527
dc.contributor.authorDubois, Didier
HAL ID: 743301
ORCID: 0000-0002-6505-2536
dc.contributor.authorCouceiro, Miguel
HAL ID: 1498
dc.date.accessioned2012-10-02T12:50:05Z
dc.date.available2012-10-02T12:50:05Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10418
dc.language.isoenen
dc.subjectDistributive latticeen
dc.subjectpolynomial functionen
dc.subjectinterpolationen
dc.subject.ddc512en
dc.titleGeneral interpolation by polynomial functions of distributive latticesen
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherUniversity of Szeged;
dc.contributor.editoruniversityotherUniversite Lyon I;
dc.contributor.editoruniversityotherIRIT;
dc.contributor.editoruniversityotherIRIT;
dc.description.abstractenFor 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.en
dc.identifier.citationpages347-355en
dc.relation.ispartofseriestitleCommunications in Computer and Information Scienceen
dc.relation.ispartofseriesnumbervol 299en
dc.relation.ispartoftitleAdvances 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 IIIen
dc.relation.ispartofeditorGreco, Salvatore
dc.relation.ispartofeditorBouchon-Meunier, Bernadette
dc.relation.ispartofeditorColetti, Giulianella
dc.relation.ispartofeditorFedrizzi, Mario
dc.relation.ispartofeditorMatarazzo, Benedetto
dc.relation.ispartofeditorYager, Ronald R.
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlinen
dc.relation.ispartofdate2012
dc.relation.ispartofpages630en
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-3-642-31718-7en
dc.subject.ddclabelAlgèbreen
dc.relation.ispartofisbn978-3-642-31717-0en
dc.relation.conftitle14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU2012)en
dc.relation.confdate2012-07
dc.relation.confcityCataneen
dc.relation.confcountryItalieen
dc.relation.forthcomingnonen
dc.identifier.doihttp://dx.doi.org/10.1007/978-3-642-31718-7_36en


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