Clean air, as a symbol of high-quality air quality, is the most basic requirement for people to maintain health. Moreover, in keeping humans fit, accurate short-term air quality prediction is vital. The decomposition algorithm can better capture the local features and temporal changes of the data. However, it increases the computation time, resource consumption, and complexity of the model. On the other hand, existing forecasting systems overlook instability and uncertainty. To solve the above problems, a deterministic and uncertainty AOA-DBGRU-MDN deep learning systems is proposed, which combines arithmetic optimization algorithm (AOA), double-layer bi-directional GRUs (DBGRU), and mixture density network (MDN). The above systems consider meteorological factors and air pollutants comprehensively. It involves feature selection using maximum information coefficient (MIC), decomposition using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm, classification, and compression of decomposed components using entropy-Huffman tree compression. Firstly, the information measurement process reduces the number of components significantly. Following the incorporation of multi-factor data, the optimal DBGRU model is then obtained using AOA. Finally, the training errors are fitted using MDN to obtain interval prediction results. The experiments demonstrate that (1) Using the CEEMDAN algorithm can improve the prediction accuracy; (2) Classifying and reconstructing the data based on entropy-Huffman tree compression can not only decrease the model's training volume and improve training efficiency but also boost the model's prediction accuracy; (3) The AOA-DBGRU-MDN system performs probabilistic prediction to obtain an effective and intuitive prediction interval to improve the point prediction of air quality prediction.