On the Normalization of Interval Data

Regivan Santiago, Flaulles Bergamaschi, Humberto Bustince, Graçaliz Dimuro, Tiago Asmus and José Antonio Sanz
Additional contact information
Regivan Santiago: Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, Brazil
Flaulles Bergamaschi: Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual do Sudoeste da Bahia, 45031-900 Vitória da Conquista, BA, Brazil
Humberto Bustince: Departamento of Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
Graçaliz Dimuro: Departamento of Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
Tiago Asmus: Departamento of Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
José Antonio Sanz: Departamento of Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain

Mathematics, 2020, vol. 8, issue 11, 1-18

Abstract: The 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.

Keywords: intervals; normalization; normalization of interval data; interval arithmetics; partition principle and interval division structures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/11/2092/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/11/2092/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:11:p:2092-:d:449551

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().