It’s just semantics.
In last month there’s been a little debate regarding whether or not the Traveling Salesman Problem (TSP) is NP-complete. Puget argues that it is not, because he’s thinking of the optimization version of TSP. Fortnow clarifies that there is a standard decision problem associated with the TSP that is NP-complete and isn’t bothered with the technicalities. Since this is my blog I’ll also link to my response.
Grötschel, Lovász, and Schrijver are sympathetic to Fortnow’s viewpoint in Geometric Algorithms and Combinatorial Optimization:
Since we do not want to elaborate on the subtle differences between the various problem classes related to the class NP we shall use the following quite customary convention. In addition to all decision problems that are NP-complete, we call every optimization problem NP-complete for which the associated decision problem is NP-complete.
I realize my opinion means nothing compared to that of greats like Fortnow, Grötschel, Lovász, and Schrijver. Still, I sit on the “let’s try to be precise” side of this debate.