What does $\mathbf{Q}^+$ mean in approximation texts?
I'm going to say yes, positive rationals, because:


That's what it means throughout math literature.
That's a sensible domain for a cost function. It would possibly be a different algorithm problem if "negative" cost were legal. Furthermore real numbers introduce questions of representation and comparing them, so while mathematicians or economists often consider real numbers for quantity, computer scientists are more cautious.
There is no front or back matter indicating otherwise.