[regularfry]

The 0..1 of fuzzy logic isn't the 0..1 of probability. When, in fuzzy logic, you say "X is true to degree 0.7" you are not saying "70% of the time, X is true" or "70% of samples display X"[0]. You are saying that the state you observe conforms to X by 70%. You can, at the same time, say "Y is true to degree 0.4". X and Y are allowed be somewhat contradictory: there's no need for their degrees to sum to 1.

[0] Not necessarily. You might choose to measure X that way, but it's not required.

[hgsgm]

You'll need to be more specific, because probability can be described the same way, numerically.

[saithound]

Fuzzy logic deals with degrees/scores, probability theory deals with how likely something is.

When you say that "The hotel room is 75% clean", that's a degree. It means a room that's not as clean as a "90% clean" hotel room, but definitely cleaner than a "50% clean" hotel room on some kind of cleanliness scale that you have. You need a scale because the boundary between clean and unclean is not sharp, but fuzzy. Fuzzy logic gives you tools to construct well-behaved scales for logical combinations of variables that already have scales associated with them. E.g. if you have a scale for a motorcycle being loud and a scale for a motorcycle being expensive (both fuzzy concepts), the tools of fuzzy logic can e.g. give you a scale for loud OR expensive.

In contrast, when you say that "The hotel room is clean with probability 75%", you're reasoning about how likely it is that the room is clean under uncertainty. Maybe the cleaners only work 3 out of 4 days, and you're unsure what day it is. But these are not degrees of cleanliness: if you say that a room has a 75% chance of being clean you're not claiming that it's cleaner than some other room that has a 50% chance of being clean.

The concepts involved in probability need not be fuzzy, or even measured on a scale. E.g. when one says "there's a 75% chance that the car repair will cost more than $50", there is no fuzziness involved in whether the repair costs more than $50 or not: in the end, you'll get a bill, and it will state a number that is unambiguously either above $50 or not above $50, a pure binary variable, no scales involved.

[doktorhladnjak]

A simple example I once heard was,

Probability: “There’s a 70% chance the grass will be wet tomorrow morning”

Fuzzy logic: “The grass will be 70% wet tomorrow morning”