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Testing statistical hypotheses with vague data. (English) Zbl 0948.62010
A definition of fuzzy test for testing statistical hypotheses with vague data is proposed. Then the general method for the construction of fuzzy tests for hypotheses concerning an unknown parameter against one-sided or two-sided alternative hypotheses is shown. This fuzzy test, contrary to the classical approach, leads not to the binary decision: to reject or to accept given null hypotheses, but to a fuzzy decision showing a grade of acceptability of the null and the alternative hypotheses, respectively. However, it is a natural generalization of the traditional test, i.e. if the data are precise, not vague, we get a classical statistical test with the binary decision. A measure of fuzziness of the considered fuzzy test is suggested and the robustness of that test is also discussed.

MSC:
62F03 Parametric hypothesis testing
62C99 Statistical decision theory
62F99 Parametric inference
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