On the use of Zadeh's probabilistic definition for testing statistical hypotheses from fuzzy information

Abstract A statistical hypothesis is an assertion about the distribution of an experiment. We consider the study of the problem of testing a statistical hypothesis (that is, the problem of concluding whether or not the hypothesis is correct) on the basis of data from the experiment, when its outcomes do not provide exact but rather fuzzy information. For establishing optimality criteria of testing we will use the definition of probability of a fuzzy event, given by Zadeh, in order to extend both Neyman-Pearson and Bayes theories, to the fuzzy framework. Then, we will analyze several properties for the new criteria. Particularly, the goodness of optimal procedures in both the fuzzy and the nonfuzzy situation, will be compared for each criterion. Finally, we will apply the extended criteria for testing simple hypotheses. This application leads us to prefer Bayesian procedures to Neyman-Pearson procedures in the fuzzy context.