PID (Proportional-Integral-Differential) control was originally developed as a form of an analog feedback control system since only analog circuits were available (of course it can now also be emulated by a digital processor).
Fuzzy logic is a digital only approach which is readily performed with a microprocessor, but not by analog circuits. In that respect, and because it's generally easier to understand, Fuzzy Logic is a good candidate to use for any microprocessor feedback-control...