A novel multi-scale fractional-order Bernoulli grey model and its application on primary school scale prediction

Primary education plays an important role in the whole educational structure. The prediction of the development scale of primary schools is of great significance to the optimal allocation of educational resources by education departments. The paper introduces a novel multi-scale fractional-order Bernoulli grey model by combining a local cumulative operator with a global cumulative operator, abbreviated as MFGM. First, a nonlinear grey Bernoulli model based on conformable fractional derivative is proposed, where a hybrid accumulation is presented. Then, the MFGM parameters are obtained by an PSO optimizer, which are adaptive to data sets. Finally, the proposed model is validated and used to predict the scale of primary school scale. Experimental results show that the MFGM is superior to the other grey models and machine learning models in the fitting and testing primary school scale. The prediction results contribute to the decision-making of education sectors.