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Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data

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Abstract

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. This paper tries to develop a new approach for testing fuzzy hypothesis when the available data are fuzzy, too. First, some definitions are provided, such as: fuzzy sample space, fuzzy-valued random sample, and fuzzy-valued random variable. Then, the problem of fuzzy hypothesis testing with vague data is formulated. Finally, we state and prove a generalized Neyman–Pearson Lemma for such problem. The proposed approach is illustrated by some numerical examples.

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Authors and Affiliations

  1. Department of Statistics, Yazd University, Yazd, Iran

    Hamzeh Torabi

  2. Department of Statistics, Islamic Azad University of Shiraz, Shiraz, Iran

    Javad Behboodian

  3. School of Mathematical Sciences, Isfahan University of Technology, 84156, Isfahan, Iran

    S. Mahmoud Taheri

Authors
  1. Hamzeh Torabi
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  2. Javad Behboodian
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  3. S. Mahmoud Taheri
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Correspondence to Hamzeh Torabi.

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Torabi, H., Behboodian, J. & Taheri, S.M. Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data. Metrika 64, 289–304 (2006). https://doi.org/10.1007/s00184-006-0049-8

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  • DOI: https://doi.org/10.1007/s00184-006-0049-8

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