Cyber-physical-social systems (CPSS), an emerging cross-disciplinary research area, combines cyber-physical systems (CPS) with social networking for the purpose of providing personalized services for humans. CPSS big data, recording various aspects of human lives, should be processed to mine valuable information for CPSS services. To efficiently deal with CPSS big data, artificial intelligence (AI), an increasingly important technology, is used for CPSS data processing and analysis. Meanwhile, the rapid development of edge devices with fast processors and large memories allows local edge computing to be a powerful real-time complement to global cloud computing. Therefore, to facilitate the processing and analysis of CPSS big data from the perspective of multi-attributes, a cloud-edge-aided quantized tensor-train distributed long short-term memory (QTT-DLSTM) method is presented in this article. First, a tensor is used to represent the multi-attributes CPSS big data, which will be decomposed into the QTT form to facilitate distributed training and computing. Second, a distributed cloud-edge computing model is used to systematically process the CPSS data, including global large-scale data processing in the cloud, and local small-scale data processed at the edge. Third, a distributed computing strategy is used to improve the efficiency of training via partitioning the weight matrix and large amounts of input data in the QTT form. Finally, the performance of the proposed QTT-DLSTM method is evaluated using experiments on a public discrete manufacturing process dataset, the Li-ion battery dataset, and a public social dataset.