Sorry for the delay, just seeing this. Yes, effectively the entirety of probability theory can be reduced to Cox's axioms of probability, which themselves are s

Sorry for the delay, just seeing this. Yes, effectively the entirety of probability theory can be reduced to Cox's axioms of probability, which themselves are specialised instances of fuzzy set/logic theory. Therefore in theory any probabilistic formulation can also be expressed in fuzzy terms with suitable constraints. E.g. I think what is implied by your final quote is the distinction between 'crisp' events and non-crisp ones. Probability only deals with crisp events. In other words, if you have a probability distribution over events, those events are required to be mutually exclusive and exhaustive for Cox's axioms of probability to apply. A fuzzy formulation can express the same problem but without that constraint, e.g. events may be 'fuzzy' (in that you might consider an 'event' with an associated 'probability / fuzzy membership in some set' of its own, but also the definition of the event itself is 'leaking out' into neighbouring events. As an example, consider a set of integers {1 .. 10}, and you want to define a probability distribution for each of the numbers on that set. A fuzzy formulation could allow you to generalise this space further using 'fuzzy integers', expressing the notion e.g. 'approximately ten'. You can then then talk about the probability of 'approximately ten' in the set (where the definition of 'approximately' is not necessarily stochastic). I'm not an expert in any of this, alas, but it does seem to me that exposure to fuzzy theory in the public seems to follow a pareto distribution, where 99% of people have only heard of ridiculously elementary uses of fuzzy theory (and therefore think it's some sort of poor-man's probability theory), which probably only accounts for something like 1% of the field, and the remaining 99% of fuzzy theory is only dealt with by 1% of people who are more preoccupied with abstract math formalizations and have no interest in practical applications (which is a shame).