Power analysis of the one sample test for fuzzy random variables

In previous works valuable tools in testing statistical hypotheses about the means of fuzzy random variables have been developed. In this paper we present a study about the power function of an asymptotic procedure for the one-sample test. More precisely, the behaviour of the statistic under local alternatives is analyzed. The procedure is carried out on the basis of a metric between fuzzy sets defined through their support functions which allows us to take advantage of the central limit theorem in Banach spaces.