Necessary efficiency is partitioned into possible and necessary optimalities

To multiple objective linear programming problems with interval objective functions, the necessarily efficient solution has been proposed as one of very reasonable solution concepts. While the relation of efficient solutions to the conventional multiple objective linear programming problem and optimal solutions to the related single objective problems is well established, the relation of the necessarily efficient solutions with possibly and necessarily optimal solutions to the related single objective problems with uncertain coefficients of the objective function has not yet been studied extensively. In this paper, we investigate the relation. We first show the insufficiency of the conventional scalarization methods for the problem with interval coefficients of objective functions. We clarify the relation of the necessarily efficient solutions with possibly and necessarily optimal solutions by the investigation of properties of necessarily efficient solutions.