Publication:
On the normalization of interval data

dc.contributor.authorSantiago, Regivan
dc.contributor.authorBergamaschi, Flaulles
dc.contributor.authorBustince Sola, Humberto
dc.contributor.authorPereira Dimuro, Graçaliz
dc.contributor.authorDa Cruz Asmus, Tiago
dc.contributor.authorSanz Delgado, José Antonio
dc.contributor.departmentEstadística, Informática y Matemáticases_ES
dc.contributor.departmentEstatistika, Informatika eta Matematikaeu
dc.date.accessioned2021-06-25T12:34:24Z
dc.date.available2021-06-25T12:34:24Z
dc.date.issued2020
dc.description.abstractThe impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact value will be enclosed in the resulting 'normalized' interval. This paper shows that this approach is not enough since the resulting 'normalized' interval can be even wider than the input intervals. So, we propose a pair of axioms that must be satisfied by an interval arithmetic in order to be applied in the normalization of intervals. We show how some known interval arithmetics behave with respect to these axioms. The paper ends with a discussion about the current paradigm of interval computations.en
dc.description.sponsorshipThis study was funded by National Council for Scientific and Technological Development (CNPq) within the project 312053/2018-5, by Coordination for the Improvement of Higher Education Personnel (CAPES) within the project Capes-Print 88887.363001/2019-00. Ministerio de Ciencia y innovación within the project PID2019-108392GB-I00 (AEI/10.13039/501100011033).en
dc.format.extent18 p.
dc.format.mimetypeapplication/pdfen
dc.identifier.doi10.3390/math8112092
dc.identifier.issn2227-7390
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/40056
dc.language.isoengen
dc.publisherMDPIen
dc.relation.ispartofMathematics, 2020, 8, 2092en
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108392GB-I00/ES/en
dc.relation.publisherversionhttps://doi.org/10.3390/math8112092
dc.rights© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.en
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectInterval arithmeticsen
dc.subjectIntervalsen
dc.subjectNormalizationen
dc.subjectNormalization of interval dataen
dc.subjectPartition principle and interval division structuresen
dc.titleOn the normalization of interval dataen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/publishedVersionen
dc.type.versionVersión publicada / Argitaratu den bertsioaes
dspace.entity.typePublication
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