Testing fuzzy hypotheses with crisp data based on p-value

Abstract

In this paper, we propose the p-value of fuzzy hypothesis by the concept of projection of the fuzzy relation, the small p-value gives evidence that research hypothesis is true. For the crisp hypothesis, we give the fuzzy set description of the test and prove that the rejection region of the test is the cut set of the fuzzy set. Finally, the p-values of fuzzy hypothesis are given by specific examples.