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Traditional techniques to prove some limit theorems for fuzzy random variables

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Statistical Modeling, Analysis and Management of Fuzzy Data

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 87))

Abstract

In the last years, some limit theorems for fuzzy random variables have been proven by means of different techniques developed for this purpose. In this work we deal with the cadlag representation of a kind of fuzzy sets to show that these limit results can be also proved by applying well-known techniques in Probability Theory (specifically, the ones which make valid the analogous theorems for D[0, 1]-valued random elements). In this context, we will study a strong law of large numbers (whose proof will suggest a characterization of the uniform convergence) and a strong law of the iterated logarithm. Furthermore, we will check the relationships between these techniques and the ones used by Molchanov to prove a SLLN for the same random elements.

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Author information

Authors and Affiliations

  1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, 33071, Oviedo, Spain

    Ana Colubi

Authors
  1. Ana Colubi
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Carlo Bertoluzza

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, C/Calvo Sotelo, s/n, 33007, Oviedo, Spain

    María-Ángeles Gil

  3. Department of Mathematical Sciences, University of Cincinnati, 45221-0025, Cincinnati, OH, USA

    Dan A. Ralescu

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© 2002 Springer-Verlag Berlin Heidelberg

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Colubi, A. (2002). Traditional techniques to prove some limit theorems for fuzzy random variables. In: Bertoluzza, C., Gil, MÁ., Ralescu, D.A. (eds) Statistical Modeling, Analysis and Management of Fuzzy Data. Studies in Fuzziness and Soft Computing, vol 87. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1800-0_4

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  • DOI: https://doi.org/10.1007/978-3-7908-1800-0_4

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2501-5

  • Online ISBN: 978-3-7908-1800-0

  • eBook Packages: Springer Book Archive

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