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Statistical simulations with LR random fuzzy numbers

Author

Listed:
  • Abbas Parchami

    (Shahid Bahonar University of Kerman)

  • Przemyslaw Grzegorzewski

    (Warsaw University of Technology
    Systems Research Institute, Polish Academy of Sciences)

  • Maciej Romaniuk

    (Systems Research Institute, Polish Academy of Sciences
    Warsaw School of Information Technology)

Abstract

Computer simulations are a powerful tool in many fields of research. This also applies to the broadly understood analysis of experimental data, which are frequently burdened with multiple imperfections. Often the underlying imprecision or vagueness can be suitably described in terms of fuzzy numbers which enable also the capture of subjectivity. On the other hand, due to the random nature of the experimental data, the tools for their description must take into account their statistical nature. In this way, we come to random fuzzy numbers that model fuzzy data and are also solidly formalized within the probabilistic setting. In this contribution, we introduce the so-called LR random fuzzy numbers that can be used in various Monte-Carlo simulations on fuzzy data. The proposed method of generating fuzzy numbers with membership functions given by probability densities is both simple and rich, well-grounded mathematically, and has a high application potential.

Suggested Citation

  • Abbas Parchami & Przemyslaw Grzegorzewski & Maciej Romaniuk, 2024. "Statistical simulations with LR random fuzzy numbers," Statistical Papers, Springer, vol. 65(6), pages 3583-3600, August.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-024-01533-5
    DOI: 10.1007/s00362-024-01533-5
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    References listed on IDEAS

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    1. 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.
    2. Ana Ramos-Guajardo & Ana Colubi & Gil González-Rodríguez & María Gil, 2010. "One-sample tests for a generalized Fréchet variance of a fuzzy random variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 185-202, March.
    3. Gholamreza Hesamian & Mohamad Ghasem Akbari & Javad Zendehdel, 2020. "Location and scale fuzzy random variables," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(2), pages 229-241, January.
    4. 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.
    5. Ramos-Guajardo, Ana Belén & Lubiano, María Asunción, 2012. "K-sample tests for equality of variances of random fuzzy sets," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 956-966.
    6. 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.
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