Incomplete information exists widely in practical engineering. How to model the incomplete information in the Dempster-Shafer evidence theory (DST) framework is still an open issue. In this paper, we present a framework on incomplete information processing in DST. We extend the model of uncertain information from the closed world assumption to the open world assumption where the incomplete information is a new type of uncertain information excluded in the closed world assumption. After that, we give a framework of incomplete information modelling and fusion in the DST framework. Finally, an example of decision-making process in air combat situation assessment with incomplete situation is introduced to show the rationality of the proposed method.