A novel GM(1,N) model based on interval gray number and its application to research on smog pollution

Purpose In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods. Design/methodology/approach This paper establishes a new graymodel (GM) (1,N) prediction modelbased on the new kernel and degree of grayness sequences under the case that the interval graynumber distribution information is known. First, the new kernel and degree of grayness sequences of the interval graynumber sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval graynumber sequence. Finally, the upper and lower bounds of the interval graynumber are deduced based on the calculation formulas of the kernel and degree of grayness. Findings To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction modelestablished in this paper has better prediction effect and accuracy. Originality/value This paper improves the traditional GM(1,N) prediction modeland establishes a new GM(1,N) prediction modelin the case of the known distribution information of the interval graynumber of the smog pollutants concentrations data.