Testing statistical hypotheses with vague data

Authors:
Przemysław Grzegorzewski
Affiliations:
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland and Institute of Mathematics, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Pol ...
Venue:
Fuzzy Sets and Systems
Year:
2000

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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.