I am currently in a Logic class and was assigned this question.
In class we define complete as a set of connectives that could generate every truth function.
My answer to this question is no, the set of logical connectives is not complete in fuzzy logic. My reasoning behind this answer is the fact that .5 is .5-preserving. You can never get anything different from a .5. More clearly,
.5 and .5 = .5
.5 or .5 = .5
Not.5 = .5
.5 implies .5 = .5
.5 if and only if .5 = .5
Is this justification enough?