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Fuzzy $$p$$-value in testing fuzzy hypotheses with crisp data. (English) Zbl 1247.62105
Summary: 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 $$p$$-values, 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.

##### MSC:
 62F86 Parametric inference and fuzziness 62F03 Parametric hypothesis testing 65C60 Computational problems in statistics (MSC2010)
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