We consider a multiobjective LP problem with interval cost matrix and fixed constraints; that is, interval uncertainty affects the objectives only. There are two natural concepts of efficiency of a solution in this case: necessary and possibly efficiency (i.e., efficiency for all or for at least one realization, respectively). We characterize these situations and present various properties, including computational complexity (the former is hard, while the latter is polynomial). As a related issue, we apply the interval methodology to a sensitivity analysis for a real-valued problem: the tolerance approach to sensitivity analysis gives ranges for the cost coefficient, in which all of them can independently vary while preserving efficiency of a given solution.