OPTIMAL STATISTICAL TESTS BASED ON FUZZY RANDOM VARIABLES

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable. The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest. For this purpose, the concepts of fuzzy test statistic and fuzzy critical value have been defined using the cuts (levels) of the fuzzy observations and fuzzy parameter. In order to make a decision as a fuzzy test, a well-known method is employed to compare the observed fuzzy test statistic and the fuzzy critical value. In this work, we focus on the case in which the fuzzy data are observations of a normal fuzzy random variable. The proposed approach is general so that it can be applied to other kinds of fuzzy random variables as well. Numerical examples, including a lifetime testing problem, are provided to illustrate the proposed optimal tests.