No. It assumes the numbers aren't random at all.
Although fuzzy-number can be used to model many different kinds of uncertainties.
I'm familiar with fuzzy numbers (e.g. see my https://filiph.net/fuzzy/ toy) but I didn't know there's arithmetic with fuzzy numbers. How is it done? Do you have a link?
There is a book by Hanss on it. It focuses on the sampling approach (he calls it "transformation method") though.
If you want to do arithmetic and not a black box approach you just have to realize that you can perform them on the alpha-cuts with ordinary interval arithmetic. Then you can evaluate arbitrary expressions involving fuzzy numbers, keeping the strengths and weaknesses of interval arithmetic.
The sampling based approach is very similar to Monte-Carlo, but you sample at certain well defined points.