A nonlinear grey model with seasonal weighted fractional accumulation for triangular fuzzy number series and its application to forecast PM2.5

Purpose Accurate prediction of PM2.5 concentration is essential for the government to formulate and implement effective environmental policies and management measures to improve air quality. PM2.5 series exhibits seasonal, nonlinear, and uncertain characteristics. A seasonal weighted fractional nonlinear grey model for triangular fuzzy number series is established based on the grey Bernoulli model by introducing the seasonal weighted fractional accumulation generating operator. Design/methodology/approach First, the actual sequence is processed using a new operator to weaken its seasonality. The sine function and the time power function are introduced into the grey Bernoulli model to perform seasonal processing on the series again, thereby enhancing the nonlinear model’s adaptability to seasonal series. Secondly, the model’s parameters are transformed into matrix form so as to directly model the triangular fuzzy number series. Additionally, the optimal algorithm is selected through algorithm comparison experiments and used to determine the nonlinear parameters. Findings Five grey models are used to predict PM2.5 concentrations in Shanghai, China and San Francisco, United States of America (USA). The findings show that the nonlinear grey model with the seasonal weighted fractional accumulation generating operator, sine function and time power function can better simulate the seasonal and nonlinear characteristics of the actual series compared to other models. Then, the PM2.5 concentrations for the next four quarters in the two cities are predicted and analyzed. Originality/value The PM2.5 concentration exhibits dynamic volatility. When represented as a triangular fuzzy number series, it better reflects the complexity and uncertainty of the data, which helps people make more accurate decisions. The model’s capacity to precisely forecast seasonal triangular fuzzy number series is improved in large part by this work.