Fuzzy logic deals with uncertainty and vagueness: a particular person may be 70% tall and 30% not-tall. Elements may be partial members of sets.
Fuzzy logic isn't just probability in disguise. That example person isn't "tall with a probability of 70%" (with the idea that if we just measured them a bit more accurately, we could know better). It's just that our mathematically sharp categories don't map that well onto the real world; fuzzy logic captures that mismatch.
Bart Kosko gives a whirlwind, and fairly non-technical, tour of fuzzy logic. He rails against the Western scientific and mathematical 'establishment' who have been dismissive of the approach, and points out that Japanese engineers have incorporated fuzzy logic in many successful products. He ends up with some speculations about how fuzzy logic might be appropriate in areas of our world and lives that don't have sharp boundaries: abortion, death, and ethics.
If you don't mind wading through all the hippy-Zen stuff, there are some interesting ideas here.