Probabilistic fuzzy system (PFS) combines a linguistic description of the system behaviour with statistical properties of data. In this paper, we propose a multi-covariate multi-output PFS for explaining and forecasting quarterly US inflation data, which shows different patterns over time such as inflation level and volatility changes. An application of a PFS to model inflation was not considered in the literature. An important aspect in inflation forecasting for macroeconomic policy makers and financial institutions is obtaining accurate forecasts for the complete inflation density together with point forecasts of inflation. We present the first PFS application where estimation and forecasting capability of PFS is assessed based on point and density forecasts. The proposed PFS model is used to forecast one, four and eight quarters ahead inflation levels and densities. Additional information provided by the different interpretations of the PFS model is used to analyse changing inflation patterns over time. The linguistic description of PFS is particularly important for the input variables which depend individuals judgement and perception. It is found that the proposed model provides accurate point and density forecasts for US inflation. In addition, changing patterns in inflation density are captured by the proposed model.