Fuzzy p-value in testing fuzzy hypotheses with crisp data

Statistical Papers volume 51, Article number: 209 (2010) Cite this article

Abstract

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first introduce the notion of fuzzy p-value, by applying the extension principle and then present an approach for testing fuzzy hypotheses by comparing a fuzzy p-value and a fuzzy significance level, based on a comparison of two fuzzy sets. Numerical examples are also provided to illustrate the approach.

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Affiliations

  1. Department of Statistics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran

    Abbas Parchami & Mashaallah Mashinchi

  2. Department of Mathematical Sciences, Isfahan University of Technology (IUT), Isfahan, 84156-83111, Iran

    S. Mahmoud Taheri

  3. Statistical Research and Training Center (SRTC), Tehran, Iran

    S. Mahmoud Taheri

Authors
  1. Abbas Parchami
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  2. S. Mahmoud Taheri
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  3. Mashaallah Mashinchi
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Correspondence to S. Mahmoud Taheri.

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Parchami, A., Taheri, S.M. & Mashinchi, M. Fuzzy p-value in testing fuzzy hypotheses with crisp data. Stat Papers 51, 209 (2010). https://doi.org/10.1007/s00362-008-0133-4

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Keywords

  • Testing hypotheses
  • Monotone likelihood ratio
  • Fuzzy hypothesis
  • Fuzzy p-value
  • Fuzzy significance level