We use a vector approach to address, from an efficient point of view, an uncertain
unconstrained multiobjective optimization problem with countably many scenarios. Specifically, we
introduce several efficient solution notions that work not only in the Pareto case, but also when the
preferences in the image space depend on the scenario and they are defined by a convex cone in the
usual way. We state basic properties of these notions and we relate the involved solution sets with
other well-known solution sets of the literature. Particularly, it is shown that the so-called highly
solutions are a particular case of efficient solutions. In addition, we obtain characterizations through
solutions of associated scalar optimization problems and we derive existence theorems. Finally, two
applications are provided to illustrate the main results.
