Defuzzification of Fuzzy p-Values

We provide a new description of the notion of fuzzy p-value, within the context of the theory of imprecise probabilities. The fuzzy p-value is viewed as a representation of a certain second-order possibility measure. According to Walley, any second-order possibility measure can be converted into a pair of lower and upper probabilities. Thus, we can convert the fuzzy p-value into an interval in the real line. We derive a construction of imprecise (but non fuzzy) tests, which are formally similar to recent tests used to manage with set-valued data.