Successful applications of fuzzy logic to reasoning in AI?
There are plenty of papers on fuzzy logic, and applications of it.

Fuzzy logic models a piece-wise control function, and is regarded as a non-linear controller. Generally, fuzzy logic can approximate any non-linear function if you divided the state-space into enough fuzzy sets.

Because it is non-linear, it is generally useful if it is controlling a non-linear system. If it were a linear system, a linear controller would be able to control it optimally already.

It is appropriate when you want to control things like movement or position (which is often the case in robots). When a system can rotate, the rotation will create the non-linearity that fuzzy logic may try to control.

In any case, the success of fuzzy logic more often has to do with how well you select the fuzzy sets (ie. their boundaries and membership functions), and how well you tune the fuzzy logic controller. In general, any controller can be successful if appropriately tuned - though their ideal performance may differ. And the most difficult part is probably tuning it - although it is not hard to get something that works, it may be hard to get something close to optimal.

If you are thinking of using a fuzzy controller, it may be a good choice if:


your system is moderately non-linear (if it is close to linear, a linear controller is sufficient)
your system is not mathematically modelled (if it is modelled, look at LQR and perhaps gain scheduling or SDRE)
or you are unsure of the parameters of your system
and any intuition of what the controller should do would be useful when trying to select the fuzzy sets and their appropriate control responses