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High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of high-tech products in Guangdong Province, China, by using a multivariable grey model.

Based on the principle of fractional order accumulation, this study proposes a multivariable grey prediction model. To further enhance the prediction ability and accuracy of the model, an optimized model is established by reconstructing the background value. The optimal parameters are solved by minimizing the average relative error of the system characteristic sequence with the constraint of parameter relationships.

The results from the study show that the two proposed models exhibit better simulation and prediction performance than the traditional models, while the optimized model can significantly improve the modelling precision. In addition, it is predicted that the output value of high-tech products is 12,269.443bn yuan in 2021, which will approximately double from 2016 to 2021.

The two proposed models can be used to forecast the trend of the system and are grown as an effective extension and supplement of the traditional multivariable grey forecasting models.

The forecast and analysis of the development prospects of high-tech industries would be useful for the government departments of Guangdong Province and professional forecasters to grasp the future of high-tech industries and formulate decision planning.

A new multivariable grey prediction model based on fractional order accumulation and its optimized model obtained by reconstructing the background value, which can improve the modelling accuracy of the traditional model, is proposed in this paper.

The purpose of this paper is to derive the analytical expression of fractional order reducing generation operator (or inverse accumulating generating operation) and study its properties.

This disaggregation method includes three main steps. First, by utilizing Gamma function expanded for integer factorial, this paper expands one order reducing generation operator into integer order reducing generation operator and fractional order reducing generation operator, and gives the analytical expression of fractional order reducing generation operator. Then, studies the commutative law and exponential law of fractional order reducing generation operator. Lastly, gives several examples of fractional order reducing generation operator and verifies the commutative law and exponential law of fractional order reducing generation operator.

The authors pull the analytical expression of fractional order reducing generation operator and verify that fractional order reducing generation operator satisfies commutative law and exponential law.

Expanding the reducing generation operator would help develop grey prediction model with fractional order operators and widen the application fields of grey prediction models.

The analytical expression of fractional order reducing generation operator, properties of commutative law and exponential law for fractional order reducing generation operator are first studied.

Electricity consumption prediction has been an important topic for its significant impact on electric policies. Due to various uncertain factors, the growth trends of electricity consumption in different cases are variable. However, the traditional grey model is based on a fixed structure which sometimes cannot match the trend of raw data. Consequently, the predictive accuracy is variable as cases change. To improve the model's adaptability and forecasting ability, a novel fractional discrete grey model with variable structure is proposed in this paper.

The novel model can be regarded as a homogenous or non-homogenous exponent predicting model by changing the structure. And it selects the appropriate structure depending on the characteristics of raw data. The introduction of fractional accumulation enhances the predicting ability of the novel model. And the relative fractional order r is calculated by the numerical iterative algorithm which is simple but effective.

Two cases of power load and electricity consumption in Jiangsu and Fujian are applied to assess the predicting accuracy of the novel grey model. Four widely-used grey models, three classical statistical models and the multi-layer artificial neural network model are taken into comparison. The results demonstrate that the novel grey model performs well in all cases, and is superior to the comparative eight models.

A fractional-order discrete grey model with an adaptable structure is proposed to solve the conflict between traditional grey models' fixed structures and variable development trends of raw data. In applications, the novel model has satisfied adaptability and predicting accuracy.

China's population aging is gradually deepening and needs to be actively addressed. The purpose of this paper is to construct a novel model for analyzing the population aging.

To analyze the aging status of a region, this study has considered three major indicators: total population, aged population and the proportion of the aged population. Additionally, the authors have developed a novel grey population prediction model that incorporates the fractional-order accumulation operator and Gompertz model (GM). By combining these techniques, the authors' model provides a comprehensive and accurate prediction of population aging trends in Jiangsu Province. This research methodology has the potential to contribute to the development of effective policy solutions to address the challenges posed by the population aging.

The fractional-order discrete grey GM is suitable for predicting the aging population and has good performance. The population aging of Jiangsu Province will continue to deepen in the next few years.

The proposed model can be used to predict and analyze aging differences in Jiangsu Province. Based on the prediction and analysis results, identified some corresponding countermeasures are suggested to address the challenges of Jiangsu's future aging problem.

The fractional-order discrete grey GM is firstly proposed in this paper and this model is a novel grey population prediction model with good performance.

The purpose of this paper is to propose a fractional order optimization method based on perturbation bound and gamma function of a DGM(r,1).

By analyzing and minimizing perturbation bound, the sub-optimal solution on fractional order interval is obtained through offline solving without iterative calculation. By this method, an optimized fractional order non-equidistant ROGM (OFONEROGM) is applied in fitting and prediction water quality parameters for a surface water pollution monitoring system.

This method can narrow fractional order interval in this work. In a surface water pollution monitoring system, the fitting and prediction performances of OFONEROGM are demonstrated comparing with integer order non-equidistant ROGM (IONEROGM).

A method of offline solving the sub-optimal solution on fractional order interval is proposed. It can narrow the optimized fractional order range of NEROGM without iterative calculation. A large number of calculations are eliminated. Besides that, optimized fractional order interval is only related to the number of original data, and convenient for practical application. In this work, an OFONEROGM is modeled for predicting water quality trend for preventing water pollution or stealing sewage discharge. It will provide guiding significance in water quality parameter fitting and predicting for water environment management.

Considering the small sample size and non-linear characteristics of historical energy consumption data from certain provinces in Southwest China, the authors propose a hybrid accumulation operator and a hybrid accumulation grey univariate model as a more accurate and reliable methodology for forecasting energy consumption. This method can provide valuable decision-making support for policy makers involved in energy management and planning.

The hybrid accumulation operator is proposed by linearly combining the fractional-order accumulation operator and the new information priority accumulation. The new operator is then used to build a new grey system model, named the hybrid accumulation grey model (HAGM). An optimization algorithm based on the JAYA optimizer is then designed to solve the non-linear parameters θ, r, and γ of the proposed model. Four different types of curves are used to verify the prediction performance of the model for data series with completely different trends. Finally, the prediction performance of the model is applied to forecast the total energy consumption of Southwest Provinces in China using the real world data sets from 2010 to 2020.

The proposed HAGM is a general formulation of existing grey system models, including the fractional-order accumulation and new information priority accumulation. Results from the validation cases and real-world cases on forecasting the total energy consumption of Southwest Provinces in China illustrate that the proposed model outperforms the other seven models based on different modelling methods.

The HAGM is used to forecast the total energy consumption of the Southwest Provinces of China from 2010 to 2020. The results indicate that the HAGM with HA has higher prediction accuracy and broader applicability than the seven comparative models, demonstrating its potential for use in the energy field.

The HAGM(1,1) is used to predict energy consumption of Southwest Provinces in China with the raw data from 2010 to 2020. The HAGM(1,1) with HA has higher prediction accuracy and wider applicability compared with some existing models, implying its high potential to be used in energy field.

Theoretically, this paper presents, for the first time, a hybrid accumulation grey univariate model based on a new hybrid accumulation operator. In terms of application, this work provides a new method for accurate forecasting of the total energy consumption for southwest provinces in China.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

Aiming to address the forecasting dilemma of seasonal air quality, the authors design the novel self-adaptive seasonal adjustment factor to extract the seasonal fluctuation information about the air quality index. Based on the novel self-adaptive seasonal adjustment factor, the novel seasonal grey forecasting models are established to predict the air quality in China.

This paper constructs a novel self-adaptive seasonal adjustment factor for quantifying the seasonal difference information of air quality. The novel self-adaptive seasonal adjustment factor reflects the periodic fluctuations of air quality. Therefore, it is employed to optimize the data generation of three conventional grey models, consisting of the GM(1,1) model, the discrete grey model and the fractional-order grey model. Then three novel self-adaptive seasonal grey forecasting models, including the self-adaptive seasonal GM(1,1) model (SAGM(1,1)), the self-adaptive seasonal discrete grey model (SADGM(1,1)) and the self-adaptive seasonal fractional-order grey model (SAFGM(1,1)), are put forward for prognosticating the air quality of all provinces in China .

The experiment results confirm that the novel self-adaptive seasonal adjustment factors promote the precision of the conventional grey models remarkably. Simultaneously, compared with three non-seasonal grey forecasting models and the SARIMA model, the performance of self-adaptive seasonal grey forecasting models is outstanding, which indicates that they capture the seasonal changes of air quality more efficiently.

Since air quality is affected by various factors, subsequent research may consider including meteorological conditions, pollutant emissions and other factors to perfect the self-adaptive seasonal grey models.

Given the problematic air pollution situation in China, timely and accurate air quality forecasting technology is exceptionally crucial for mitigating their adverse effects on the environment and human health. The paper proposes three self-adaptive seasonal grey forecasting models to forecast the air quality index of all provinces in China, which improves the adaptability of conventional grey models and provides more efficient prediction tools for air quality.

The self-adaptive seasonal adjustment factors are constructed to characterize the seasonal fluctuations of air quality index. Three novel self-adaptive seasonal grey forecasting models are established for prognosticating the air quality of all provinces in China. The robustness of the proposed grey models is reinforced by integrating the seasonal irregularity. The proposed methods acquire better forecasting precisions compared with the non-seasonal grey models and the SARIMA model.

The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(a, n) based on the classical GM(1, n) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.

The GM(α, n) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(a, n) model.

The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n), GM(a, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(a, n) model provides accurate prediction.

The GM(a, n) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(a, n) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.

It is the first time to investigate the multivariate fractional grey GM(α, n) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.

Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.