A novel fractional Hausdorff grey system model and its applications

Grey system models have proven to be effective techniques in diverse fields and are crucial to global decision science. Amongst the various approaches of grey theory, the fractional-order grey model is fundamental and extends the cumulative generation method used in grey theory. Fractional-order cumulative generating operator offers numerous significant benefits, especially in educational funding that is often influenced by economic policies. However, their computational complexity complicates the generalization of fractional-order operators in real-world scenarios. In this paper, an enhanced fractional-order grey model is proposed based on a new fractional-order accumulated generating operator. The newly introduced model estimates parameters by utilizing the method of least squares and determines the order of the model through the implementation of metaheuristic algorithms. Our results show that, after conducting both Monte Carlo simulations and practical case analyses, the newly proposed model outperforms both existing grey prediction models and machine learning models in small sample environments, thus demonstrating superior forecast accuracy. Moreover, our experiments reveal that the proposed model has a simpler structure than previously developed grey models and achieves greater prediction accuracy.