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On the Normalization of Interval Data

Author

Listed:
  • 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
    Centro de Ciências Computacionais, Universidade Federal do Rio Grande, 96203-900 Rio Grande do Sul, Brazil)

  • Tiago Asmus

    (Departamento of Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
    Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, 96203-900 Rio Grande do Sul, Brazil)

  • José Antonio Sanz

    (Departamento of Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain)

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.

Suggested Citation

  • Regivan Santiago & Flaulles Bergamaschi & Humberto Bustince & Graçaliz Dimuro & Tiago Asmus & José Antonio Sanz, 2020. "On the Normalization of Interval Data," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2092-:d:449551
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    References listed on IDEAS

    as
    1. Martha Lucia Orozco-Gutierrez, 2020. "An Interval-Arithmetic-Based Approach to the Parametric Identification of the Single-Diode Model of Photovoltaic Generators," Energies, MDPI, vol. 13(4), pages 1-22, February.
    2. Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
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