Graphical abstractDisplay Omitted HighlightsThe model of uncertain multiobjective programming based on uncertainty theory is originally presented, and six concepts of efficient solutions are defined.The relations among the efficiency concepts are established under the assumed conditions.We apply the uncertain multiobjective optimization methods to a real-life problem, i.e., the uncertain multiobjective redundancy allocation problem.A modified multiobjective artificial bee colony (MOABC) algorithm is designed to generate Pareto efficient set to the UMRA problem. Based on uncertainty theory, we investigate the relations among efficiency concepts of the multiobjective programming (MOP) with uncertain vectors. We first propose the uncertain MOP model, and study its convexity. Then, we define different efficiency concepts such as expected-value efficiency, expected-value proper efficiency, and establish their relations under the assumed conditions, which are illustrated through two numerical examples. Finally, in the uncertain environment, we apply the theoretical results to a redundancy allocation problem with two objectives in reparable parallel-series systems, and discuss how to obtain different types of efficient solutions according to the decision-maker's preferences.