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Testing hypotheses with fuzzy data: The fuzzy p-value

Author

Listed:
  • P. Filzmoser
  • R. Viertl

Abstract

Statistical hypothesis testing is very important for finding decisions in practical problems. Usually, the underlying data are assumed to be precise numbers, but it is much more realistic in general to consider fuzzy values which are non-precise numbers. In this case the test statistic will also yield a non-precise number. This article presents an approach for statistical testing at the basis of fuzzy values by introducing the fuzzy p-value. It turns out that clear decisions can be made outside a certain interval which is determined by the characterizing function of the fuzzy p-values. Copyright Springer-Verlag 2004

Suggested Citation

  • P. Filzmoser & R. Viertl, 2004. "Testing hypotheses with fuzzy data: The fuzzy p-value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 21-29, February.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:1:p:21-29
    DOI: 10.1007/s001840300269
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    Citations

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    Cited by:

    1. Abbas Parchami & S. Mahmoud Taheri & Reinhard Viertl & Mashaallah Mashinchi, 2018. "Minimax test for fuzzy hypotheses," Statistical Papers, Springer, vol. 59(4), pages 1623-1648, December.
    2. Muhammad Aslam, 2022. "Neutrosophic F-Test for Two Counts of Data from the Poisson Distribution with Application in Climatology," Stats, MDPI, vol. 5(3), pages 1-11, August.
    3. Hsu, Bi-Min & Shu, Ming-Hung, 2008. "Fuzzy inference to assess manufacturing process capability with imprecise data," European Journal of Operational Research, Elsevier, vol. 186(2), pages 652-670, April.
    4. S. Taheri & G. Hesamian, 2013. "A generalization of the Wilcoxon signed-rank test and its applications," Statistical Papers, Springer, vol. 54(2), pages 457-470, May.
    5. Viertl, Reinhard, 2006. "Univariate statistical analysis with fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 133-147, November.
    6. Shima Yosefi & Mohsen Arefi & Mohammad Ghasem Akbari, 2016. "A new approach for testing fuzzy hypotheses based on likelihood ratio statistic," Statistical Papers, Springer, vol. 57(3), pages 665-688, September.
    7. Jung-Lin Hung & Cheng-Che Chen & Chun-Mei Lai, 2020. "Possibility Measure of Accepting Statistical Hypothesis," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    8. Lubiano, María Asunción & Montenegro, Manuel & Sinova, Beatriz & de la Rosa de Sáa, Sara & Gil, María Ángeles, 2016. "Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications," European Journal of Operational Research, Elsevier, vol. 251(3), pages 918-929.
    9. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2012. "Testing fuzzy hypotheses based on vague observations: a p-value approach," Statistical Papers, Springer, vol. 53(2), pages 469-484, May.
    10. Wu, Chien-Wei, 2009. "Decision-making in testing process performance with fuzzy data," European Journal of Operational Research, Elsevier, vol. 193(2), pages 499-509, March.
    11. Nataliya Chukhrova & Arne Johannssen, 2020. "Randomized versus non-randomized hypergeometric hypothesis testing with crisp and fuzzy hypotheses," Statistical Papers, Springer, vol. 61(6), pages 2605-2641, December.
    12. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2010. "Fuzzy p-value in testing fuzzy hypotheses with crisp data," Statistical Papers, Springer, vol. 51(1), pages 209-226, January.

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