Very useful. Many problems are more easily represented as fuzzy sets or fuzzy relations than in other terms. It's particularly good at encoding linguistic variables, such as "very fast", "too cold", "accelerate hard" and so on in a way that it can smoothly overlap them.

It's also useful for encoding uncertainties that are not yet mutually exclusive. There are other logics too (eg Dempster-Shafer evidence theory), often grouped together as "monotone measures".