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Testing hypotheses with fuzzy data: The fuzzy $$p$$-value. (English) Zbl 1052.62009
Summary: 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.

##### MSC:
 62C99 Statistical decision theory 62F03 Parametric hypothesis testing 03E72 Theory of fuzzy sets, etc.
##### Keywords:
fuzzy data; non-precise numbers; $$p$$-value
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