Air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction

Abstract Performing scientific and accurate forecasting and realizing the quantitative description of uncertainties in air quality remain challenging prospects. Because of the strong volatility and uncertainty of air pollutant concentrations, this problem increases in difficulty when multiple requirements are considered. In this study, a novel air quality deterministic and probabilistic forecasting system based on hesitant fuzzy sets and nonlinear robust outlier correction was proposed to realize air quality early warning. The proposed system solves the non-stochastic non-deterministic problem in air quality forecasting considering a novel hesitant fuzzy time series forecasting model wherein the intervals are partitioned by different approaches with optimal weights determined by the multi-objective JAYA algorithm. The forecasting performance is further enhanced with the introduction of a new nonlinear error correction model based on an outlier robust extreme learning machine and multi-objective JAYA algorithm, and the quality of the solution obtained is verified by sensitivity analysis. However, point forecast information alone is not sufficient to facilitate the rational integration of pollution control measures. Therefore, this study conducts probabilistic forecasting and constructs proper prediction intervals based on the optimal distribution of the forecasting residuals. By comparing the results with typical counterparts and comparison models considering multiple metrics, the experimental results confirmed the improvement scheme proposed in this study on the traditional fuzzy time series forecasting method while the effectiveness of applying the proposed system to air quality early warning was confirmed as well.