Generalized fractional grey system models: Memory effects perspective

TL;DR

This paper develops a unified fractional grey system modeling framework incorporating memory effects, enhancing prediction accuracy and versatility through kernel functions and intelligent algorithms, validated by real-world examples.

Contribution

It introduces a novel unified framework for fractional grey models that integrates memory effects and various kernel functions, improving prediction performance.

Findings

The UFGM(1,1) model effectively predicts practical data.

Memory effects significantly influence model accuracy.

Intelligent algorithms optimize model coefficients.

Abstract

As an essential characteristics of fractional calculus, the memory effect is served as one of key factors to deal with diverse practical issues, thus has been received extensive attention since it was born. By combining the fractional derivative with memory effects and grey modeling theory, this paper aims to construct an unified framework for the commonly-used fractional grey models already in place. In particular, by taking different kernel and normalization functions, this framework can deduce some other new fractional grey models. To further improve the prediction performance, the four popular intelligent algorithms are employed to determine the emerging coefficients for the UFGM(1,1) model. Two published cases are then utilized to verify the validity of the UFGM(1,1) model and explore the effects of fractional accumulation order and initial value on the prediction accuracy, respectively. Finally, this model is also applied to dealing with two real examples so as to further explain its efficacy and equally show how to use the unified framework in practical applications.