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On Convergence in Distribution of Fuzzy Random Variables

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Building Bridges between Soft and Statistical Methodologies for Data Science (SMPS 2022)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1433))

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Abstract

We study whether convergence in distribution of fuzzy random variables, defined as the weak convergence of their probability distributions, is consistent with the additional structure of spaces of fuzzy sets. Positive results are obtained which reinforce the viability of that definition.

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References

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Acknowledgements

Research in this paper was partially funded by grants and fellowships from Spain (PID2019-104486GB-I00), the Principality of Asturias (SV-PA-21-AYUD/2021/50897 and PA-21-PF-BP20-112), and the University of Oviedo (PAPI-20-PF-21). Their contribution is gratefully acknowledged.

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Authors and Affiliations

  1. Escuela Politécnica de Ingeniería, Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Oviedo, Spain

    Miriam Alonso de la Fuente & Pedro Terán

Authors
  1. Miriam Alonso de la Fuente
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  2. Pedro Terán
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Corresponding author

Correspondence to Miriam Alonso de la Fuente .

Editor information

Editors and Affiliations

  1. Departamento de Estadística e I.O., University of Valladolid, Valladolid, Spain

    Luis A. García-Escudero

  2. Departamento de Estadística e I.O., University of Valladolid, Valladolid, Spain

    Alfonso Gordaliza

  3. Departamento de Estadística e I.O., University of Valladolid, Valladolid, Spain

    Agustín Mayo

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

    María Asunción Lubiano Gomez

  5. Departamento de Estadística, I.O. y D.M., University of Oviedo, Oviedo, Spain

    Maria Angeles Gil

  6. Department of Computational Statistics and Data Analysis, Warsaw University of Technology, Warsaw, Poland

    Przemyslaw Grzegorzewski

  7. Department of Stochastic Methods, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Olgierd Hryniewicz

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Alonso de la Fuente, M., Terán, P. (2023). On Convergence in Distribution of Fuzzy Random Variables. In: García-Escudero, L.A., et al. Building Bridges between Soft and Statistical Methodologies for Data Science . SMPS 2022. Advances in Intelligent Systems and Computing, vol 1433. Springer, Cham. https://doi.org/10.1007/978-3-031-15509-3_2

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