[tr352]

In addition to the other replies here, one fundamental difference between probabilistic and fuzzy logic is that fuzzy logic is truth functional and probabilistic logic isn't. Truth functional means, for instance, that if we know the (numerical) truth values of the propositions A and of B then we also know the (numerical) truth values of the propositions (A and B), (A or B), and so on. In probabilistic logic this does not hold. That is, P(A and B) is not fully determined by P(A) and P(B). If A and B are independent, we have P(A and B) = P(A)P(B), but in general we only know that P(A)+P(B)-1 <= P(A and B) <= min(P(A),P(B)). I also believe there's no generally accepted notion of conditioning in fuzzy logic, whereas conditioning is crucial in any probabilistic approach, see e.g. Bayes' theorem.

[regularfry]

Truth functionality always struck me as a bodge in fuzzy logic, because you get to choose the implementation of (A and B) fairly arbitrarily. You're getting to choose some mix that lets you pretend the degree of dependence between the variables doesn't matter. It's a useful engineering hack, but a hack nonetheless.