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Context, the pieces of information that capture the characteristics of ubiquitous computing environment, is often imprecise and incomplete due to user mobility, unreliable wireless connectivity and resource constraints. While many context reasoning schemes have been proposed to assist ubiquitous applications, these schemes often suffer from the assumption that the contexts are complete and precise. The main challenge for context reasoning is how to interpret and infer contexts from existing contexts that are imprecise and incomplete. To this end, we propose the DSCRtimes approach - extended Dempster-Shafer theory for context reasoning, which applies Dempster-Shafer theory to ubiquitous computing environments by following a new context-aware architecture. DSCRtimes solves the fundamental problem in Dempster-Shafer theory - intensive computation through evidence selection strategy. This strategy takes advantage of the k-l algorithm to select evidence with the highest beliefs, which considerably reduces the computation overhead. The proposed approach is evaluated through extensive experiments. The results show that DSCRtimes is appropriate to reason contexts from incomplete and imprecise contexts in ubiquitous computing environments.