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Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Author

Listed:
  • María Casals
  • Norberto Corral
  • María Gil
  • María López
  • María Lubiano
  • Manuel Montenegro
  • Gloria Naval
  • Antonia Salas

Abstract

Since Bertoluzza et al.’s metric between fuzzy numbers has been introduced, several studies involving it have been developed. Some of these studies concern equivalent expressions for the metric which are useful for either theoretical, practical or simulation purposes. Other studies refer to the potentiality of Bertoluzza et al.’s metric to establish statistical methods for the analysis of fuzzy data. This paper shortly reviews such studies and examine part of the scientific impact of the metric. Copyright Sapienza Università di Roma 2013

Suggested Citation

  • María Casals & Norberto Corral & María Gil & María López & María Lubiano & Manuel Montenegro & Gloria Naval & Antonia Salas, 2013. "Bertoluzza et al.’s metric as a basis for analyzing fuzzy data," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 307-322, November.
    • Handle: RePEc:spr:metron:v:71:y:2013:i:3:p:307-322
    DOI: 10.1007/s40300-013-0023-y
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    References listed on IDEAS

    as
    1. Gil, Maria Angeles & Montenegro, Manuel & Gonzalez-Rodriguez, Gil & Colubi, Ana & Rosa Casals, Maria, 2006. "Bootstrap approach to the multi-sample test of means with imprecise data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 148-162, November.
    2. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
    3. A. Blanco-Fernández & A. Ramos-Guajardo & A. Colubi, 2013. "Fuzzy representations of real-valued random variables: applications to exploratory and inferential studies," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 245-259, November.
    4. Manuel Montenegro & Ana Colubi & María Rosa Casals & María Ángeles Gil, 2004. "Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 31-49, February.
    5. Gil, Maria Angeles & Gonzalez-Rodriguez, Gil & Colubi, Ana & Montenegro, Manuel, 2007. "Testing linear independence in linear models with interval-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3002-3015, March.
    6. Gonzalez-Rodriguez, Gil & Colubi, Ana & Angeles Gil, Maria, 2006. "A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 163-176, November.
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