(positives:)

Fuzzy Logic has some utility in engineering applications, because it can be intuitive for humans interpret and to create rules using it. Interpretability is also the strong point of neuro-fuzzy logic (hybrid system). Applications are usually control systems, business logic, or embedded systems with tight resource constraints.

(negatives:)

In academic research it's not that interesting, because it's just one multi-valued logic among others, subset of infinite-valued logic. It's not very useful in machine learning because there are no efficient way to learn fuzzy rules automatically.