The conformable fractional grey system model

Abstract

The fractional order grey models (FGM) have appealed considerable interest of research in recent years due to its higher effectiveness and flexibility than the conventional grey models and other prediction models. However, the definitions of the fractional order accumulation (FOA) and difference (FOD) is computationally complex, which leads to difficulties for the theoretical analysis and applications. In this paper, the new definition of the FOA are proposed based on the definitions of Conformable Fractional Derivative, which is called the Conformable Fractional Accumulation (CFA), along with its inverse operation, the Conformable Fractional Difference (CFD). Then the new Conformable Fractional Grey Model (CFGM) based on CFA and CFD is introduced with detailed modelling procedures. The feasibility and simplicity and the CFGM are shown in the numerical example. And the at last the comprehensive real-world case studies of natural gas production forecasting in 11 countries are presented, and results show that the CFGM is much more effective than the existing FGM model in the 165 subcases.

An improved gray prediction model for China’s beef consumption forecasting

“…However, although the gray prediction model has made great progress in its modeling mechanism and performance optimization since the 1980s[3, 32] and some new practical gray system models have been developed [33–34], there are still some problems with the structural and parameter optimization of the traditional gray prediction model [35–40]. Therefore, an improved gray model termed, EGM(1,1, r ), is built, and the modeling conditions and error checking methods of EGM(1,1, r ) are studied.…”

Modeling Method of the Grey GM(1,1) Model with Interval Grey Action Quantity and Its Application

“…(a) Optimization of GM(1,1) parameters: such as initial condition optimization [13,14], background value optimization [15,16], and accumulation order optimization [17][18][19] (b) Optimization of GM(1,1) structure: realizing the optimization of model structure from the single exponential form to intelligent variable structure [20][21][22] (c) Extension of GM(1,1) modeling object: to achieve the expansion of modeling objects from real data to grey uncertain data [23][24][25] (d) GM (1,1) combined forecasting model: the combination prediction technologies of GM (1,1) and other methods are studied, such as Grey neural network model [26][27][28], Grey Markov model [29,30], Grey support vector machine [31,32], and Grey deep learning [33,34] e above research results play an important role in improving the simulation and prediction performance and expanding the application scope of GM (1,1). However, GM(1,1) is a grey model with incomplete structural information (the absence of independent variables).…”

Coupling a Bat Algorithm with XGBoost to Estimate Reference Evapotranspiration in the Arid and Semiarid Regions of China

“…Artificial intelligence (AI) algorithms are becoming popular recently because of their high flexibility and precision and have been applied widely in fields of hydrology, agriculture, and environment [5][6][7][8], such as drought forecasting [9], solar radiation modeling [2,10], temperature estimation [11], precipitation modeling [12], soil moisture simulation [13], and reference evapotranspiration estimation [14][15][16][17]. In the early years, artificial neural networks (ANNs) were used to simulate ETo, generating more accurate results than the empirical model [18].…”