Fuzzy "logic" is best used when you take out all the references to logic and just think about fuzzy sets -- then it's just fuzzy set theory, which is useful when you need to model partial set membership.

I enjoyed reading Probabilistic Logic Networks (https://www.amazon.com/Probabilistic-Logic-Networks-Comprehe...) as it introduces a possible framework to sanely deal with different kinds of truth values about different things which aren't necessarily a single number.