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A new approach for testing fuzzy hypotheses based on likelihood ratio statistic

Author

Listed:
  • Shima Yosefi

    (University of Birjand)

  • Mohsen Arefi

    (University of Birjand)

  • Mohammad Ghasem Akbari

    (University of Birjand)

Abstract

In this paper, a new approach for testing fuzzy hypotheses based on likelihood ratio test statistic is presented. In this approach, we first formulate the hypotheses of interest by fuzzy sets, and then, a likelihood ratio statistic is defined based on the $$\delta $$ δ -cut of null fuzzy hypothesis. Also, in order to establish critical region, we give new definitions for the probabilities of type I and type II errors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0673-3
    DOI: 10.1007/s00362-015-0673-3
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    References listed on IDEAS

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    1. Bernhard Arnold, 1996. "An approach to fuzzy hypothesis testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 119-126, December.
    2. 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.
    3. Hamzeh Torabi & Javad Behboodian, 2007. "Likelihood ratio tests for fuzzy hypotheses testing," Statistical Papers, Springer, vol. 48(3), pages 509-522, September.
    4. 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.
    5. 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.
    6. Hamzeh Torabi & Javad Behboodian & S. Taheri, 2006. "Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(3), pages 289-304, December.
    7. 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.
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    Cited by:

    1. 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.

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