I do want to note that probabilities 0 and 1 only correspond to no fuzziness if we assume a finite set. If we don’t assume a finite set, then it’s easy to cook up examples where probabilities are 0 or 1, but they aren’t equivalent to either nothing or everything, and thus probabilities 0 or 1 can still introduce fuzziness.
I do want to note that probabilities 0 and 1 only correspond to no fuzziness if we assume a finite set. If we don’t assume a finite set, then it’s easy to cook up examples where probabilities are 0 or 1, but they aren’t equivalent to either nothing or everything, and thus probabilities 0 or 1 can still introduce fuzziness.