A Bootstrap Test for the Expectation of Fuzzy Random Variables

We consider the problem of testing a single hypothesis about the expectation of a fuzzy random variable. For this purpose we take as test statistic a distance between the sample mean and the mean in the null hypothesis. We show that the test rejecting the null hypothesis for large values of the test statistic is consistent. We also prove that the bootstrap can be employed to consistently approximate the null distribution of the test statistic. Finally, we study the finite sample performance of the proposed approximation and compare it with others by means of a simulation study.