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Decision-making in dense traffic scenarios is challenging for automated vehicles (AVs) due to potentially stochastic behaviors of other traffic participants and perception uncertainties (e.g., tracking noise and prediction errors, etc.). Although the partially observable Markov decision process (POMDP) provides a systematic way to incorporate these uncertainties, it quickly becomes computationally intractable when scaled to the real-world large-size problem. In this paper, we present an efficient uncertainty-aware decision-making (EUDM) framework, which generates long-term lateral and longitudinal behaviors in complex driving environments in real-time. The computation complexity is controlled to an appropriate level by two novel techniques, namely, the domain-specific closed-loop policy tree (DCP-Tree) structure and conditional focused branching (CFB) mechanism. The key idea is utilizing domain-specific expert knowledge to guide the branching in both action and intention space. The proposed framework is validated using both onboard sensing data captured by a real vehicle and an interactive multi-agent simulation platform. We also release the code of our framework to accommodate benchmarking.