Accurate forecasting of the air quality index (AQI) plays a crucial role in taking precautions against upcoming air pollution risks. However, air quality may fluctuate greatly in a certain period. Existing forecasting approaches always face the problem of losing valuable information on air quality status, even in the interval models of recent research. To address this issue, this paper suggests a new AQI forecasting perspective and paradigm built upon ternary interval-valued time series (TITS), multivariate variational mode decomposition (MVMD), multivariate relevance vector machine (MVRVM), mixed coding particle swarm optimization (MCPSO), and meteorological factors, which is able to capture the trend and volatility changes of AQI concurrently. The proposed paradigm involves four procedures: TITS construction in terms of the daily minimum, daily mean, and daily maximum AQI, multi-scale decomposition via MVMD, individual forecasting by MCPSO-optimized MVRVM, and ensemble learning forecasting using a simple addition approach. Experiments based on datasets collected from four municipalities in China demonstrated that the presented paradigm can hit higher accuracy than other comparable models, and the application analysis also shows that it has application potential in the AQI online forecasting system. To conclude, the proposed paradigm provides a promising alternative for AQI time series forecasting.