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On the Robustness of Absolute Deviations with Fuzzy Data

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Strengthening Links Between Data Analysis and Soft Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 315))

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Abstract

Often atypical observations separated from the majority or deviate from the general pattern appear in the datasets. Classical estimators such as the sample mean or the sample variance, can be substantially affected by these observations, which are referred to as outliers. Robust statistics provides methods which are not unduly influenced by atypical data.

In this paper an introductory empirical study is developed to compare the robustness of the scale estimator ‘Median Absolute Deviation’ in contrast to the classical scale estimator ‘Average Absolute Deviation’ in a fuzzy setting. Both estimators are defined on the basis of the Aumann-type mean, the 1-norm median for random fuzzy numbers along with an L 1-type metric between fuzzy numbers, and some of their properties are examined. Outliers will be introduced in simulated fuzzy data to analyze how much these two estimators are influenced by them.

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Author information

Authors and Affiliations

  1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, 33007, Oviedo, Spain

    Sara de la Rosa de Sáa, María Ángeles Gil & María Asunción Lubiano

  2. Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität Wien, 1040, Wien, Austria

    Peter Filzmoser

Authors
  1. Sara de la Rosa de Sáa
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  2. Peter Filzmoser
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  3. María Ángeles Gil
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  4. María Asunción Lubiano
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Corresponding author

Correspondence to Sara de la Rosa de Sáa .

Editor information

Editors and Affiliations

  1. Polish Academy of Sciences, Faculty of Mathematics and Information Sciences, Systems Research Institute and Warsaw University of Technology, Warsaw, Poland

    Przemyslaw Grzegorzewski

  2. Polish Academy of Sciences, Faculty of Mathematics and Information Sciences, Systems Research Institute and Warsaw University of Technology, Warsaw, Poland

    Marek Gagolewski

  3. Polish Academy of Sciences Systems Research Institute, Warsaw, Poland

    Olgierd Hryniewicz

  4. Departamento de Estadistica e I.O. y D.M., University of Oviedo, Oviedo, Spain

    María Ángeles Gil

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de la Rosa de Sáa, S., Filzmoser, P., Gil, M.Á., Lubiano, M.A. (2015). On the Robustness of Absolute Deviations with Fuzzy Data. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-10765-3_16

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10764-6

  • Online ISBN: 978-3-319-10765-3

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