[sacado2]

Since we're talking about non-classical logics, I also like modal logic, which deals with uncertainty too, but in a very different way. Here, facts / assertions are not associated with a numeric value, but with a modality, a symbol, meaning "it is possible that F is true", "it is not necessary that F is true", "F is usually true", "F was true yesterday", or "I know I don't know whether F is true or false".

https://en.wikipedia.org/wiki/Modal_logic

It has interesting properties, and it avoids the main pitfal of fuzzy logic IMO: when a fact is associated with a truth value of 0.8, what does that really mean? Why is the truth value 0.8 rather than 0.81, for instance? Can we say so for sure?

[jacques_chester]

The truth value being 0.8 can be mapped to one or more fuzzy sets. That's what you're typically doing. Saying "I don't know" is still possible, because you can define a fuzzy set representing "I don't know". But now you can say how strongly you don't know.

An overlapping alternative is Dempster-Shafer evidence theory, which has "belief functions" and rules on how to combine them.