Inclusion and exclusion hypothesis tests for the fuzzy mean

A hypothesis test for the inclusion of the expected value of a fuzzy-valued random element in a given fuzzy set is provided. The exclusion, or the empty intersection of the expected value of a random fuzzy set and a fuzzy set, is also tested, that allows us to define one-sided tests for this expected value without the need of considering any restrictive ordering. Both tests are developed by using a measure of the intersection between fuzzy sets. Asymptotic and bootstrap techniques are established. Some simulations are included to show the performance of the bootstrap approaches. Finally, the methodology proposed is applied on a real-life situation related to the field of sensorial analysis.