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Testing fuzzy hypotheses with crisp data. (English) Zbl 0940.62015
Summary: An approach is presented how statistical tests originally constructed to examine crisp hypotheses can also be applied to fuzzily formulated hypotheses. In particular, criterions $$\alpha$$ and $$\beta$$ are proposed generalizing the probabilities of the errors of type I and type II, respectively. The general approach is applied to one- and two-sided Gauß tests. Here, diagrams are given to determine the critical values in the most popular cases of $$\alpha=0.01$$ and $$\alpha=0.05$$. If, in addition, the value of $$\beta$$ is fixed in advance the sample size of a one- or two-sided Gauß test can be obtained using supplementary graphs.

##### MSC:
 62F03 Parametric hypothesis testing 62F99 Parametric inference
##### Keywords:
fuzzy hypotheses; sample size; Gauß tests
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##### References:
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