Fuzzy sets allow you to use set theoretic tools over objects with varying degrees of membership. This is a useful construct when trying to reason over probabilistic evidence, and IMO can be a useful modelling tool.
you can also do exactly that in probability theory by multiplying the probabilities. Is there any difference?
Have you got a concrete example?
i.e., show us the probability version precisely with mathematics and maybe someone can tell you the corresponding fuzzy version, if any.