An Optimized Fractional Nonlinear Grey System Model and Its Application in the Prediction of the Development Scale of Junior Secondary Schools in China

Abstract

As part of China’s compulsory nine-year education system, junior secondary education (JSSE) plays a vital role in supporting students’ physical and mental development. The accurate prediction of the development scale trend of JSSE is helpful for the government to estimate the scale of educational development within a chosen time frame so as to aid decision making.Nevertheless, China’s education system is complex, highly dimensional, and largely influenced by policy and other factors, which results in difficulty in modeling the education sample. Based on gray system theory, this paper proposes an improved fractional-order grey prediction model, OCFNGBM(1,1), to predict the development scale of JSSE. We describe the basic expressions of the model, the parameter estimation method, and the optimization method for hyperparameters and construct a scheme for optimizing the background value coefficients. Data collected from official websites from 2011 to 2021 are used to build the forecasting model, and data from 2011 to 2017 are used to evaluate the model’s accuracy. Our experimental results indicate that the OCFNGBM(1,1) model has higher accuracy than the classical nonlinear gray prediction model. The OCFNGBM(1,1) model was employed to forecast the development scale of JSSE in China from 2022 to 2024, which provided useful information. This research provides a resource to help the national education department to develop a comprehensive and long-term plan for the development goals, scale, speed, steps, and measures of relevant education.