Elsevier

Fuzzy Sets and Systems

Volume 112, Issue 3, 16 June 2000, Pages 501-510
Fuzzy Sets and Systems

Testing statistical hypotheses with vague data

https://doi.org/10.1016/S0165-0114(98)00061-XGet rights and content

Abstract

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 hypothesis, but to a fuzzy decision showing a grade of acceptability of the null and the alternative hypothesis, 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.

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