I'm learning about fuzzy logic and fuzzy sets, and it seems to me that there is no requirement that there be at least one element in the domain set for which the membership function is equal to 1. That is, can this statement possibly be true?
$ \{ x \in X: A(x) = 1 \} = \emptyset $
Where $X$ is a universal set and $A(x)$ is a membership function (denoting membership of an arbitrary set $A$).
If so, what would be a real-world example of such a fuzzy membership function?
Actually the answer is yes...
For example, consider the set of tennis ball colours in a 4-ball canister. Are they fluoro yellow or fluoro green...? The colour of each ball - arguably - has non-zero membership in each each of these two sets, but not complete membership in either.