If a Concept Itself Is Vague, Can It Still Have

If a concept itself is vague, can it still have a logical definition?

A) No, because logical definitions don't allow for vagueness.
B) No, because it would be impossible to find the right genus for a vague concept.
C) Yes, but the definition would also be vague.
D) Yes, but the definition would end up being circular.
E) Yes, but the definition would end up being too broad or too narrow.