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We extend the classical approach of hypothesis testing to the fuzzy environment. We propose a method based on fuzziness of data and on fuzziness of hypotheses at the same time. The fuzzy p-value with its α-cuts is provided and we show how to defuzzify it by the signed distance method. We illustrate our method by numerical applications where we treat a one and a two sided test. For the one-sided test, applying our method to the same data and performing tests on the same significance level, we compare the defuzzified p-values between different cases of null and alternative hypotheses.

Testing Fuzzy Hypotheses with Fuzzy Data and Defuzzification of the Fuzzy p-value by the Signed Distance Method