Defuzzification of Fuzzy p-Values

TitleDefuzzification of Fuzzy p-Values
Publication TypeConference Paper
Year of Publication2008
AuthorsCouso, Inés, and Sánchez Luciano
EditorDubois, Didier, M. Lubiano Asunción, Prade Henri, Gil María Ángeles, Grzegorzewski Przemysław, and Hryniewicz Olgierd
Conference NameSoft Methods for Handling Variability and Imprecision
PublisherSpringer Berlin Heidelberg
Conference LocationBerlin, Heidelberg
ISBN Number978-3-540-85027-4

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.