Fuzzy decision in testing hypotheses by fuzzy data: Two case studies

In testing hypotheses, we may confront with cases where data are recorded as non-precise (fuzzy) rather than crisp. In such situations, the classical methods of testing hypotheses are not capable and need to be generalized. In solving the problem of testing hypotheses based on fuzzy data, the fuzziness of the observed data leads to the fuzzy p-value. This paper has been focused to calculate fuzzy p-value based on fuzzy data using the extension principle. Also, considering that p-value method is the most widely used / popular approach for testing hypotheses among different sciences users, two fuzzy $p$-value-based case studies have been provided in this paper. The first case study is discussed on ″the fuzzy data from a speedometer camera" and the second is deliberate about ″the lifetime of produced batteries in a factory" and both of them have been solved by a novel approach considering other studies found in the literature.