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Forecasting outpatient volume during a significant security crisis can provide reasonable decision-making references for hospital managers to prevent sudden outbreaks and dispatch medical resources on time. Based on the background of standard hospital operation and Coronavirus disease (COVID-19) periods, this paper constructs a hybrid grey model to forecast the outpatient volume to provide foresight decision support for hospital decision-makers.

This paper proposes an improved hybrid grey model for two stages. In the non-COVID-19 stage, the Aquila Optimizer (AO) is selected to optimize the modeling parameters. Fourier correction is applied to revise the stochastic disturbance. In the COVID-19 stage, this model adds the COVID-19 impact factor to improve the grey model forecasting results based on the dummy variables. The cycle of the dummy variables modifies the COVID-19 factor.

This paper tests the hybrid grey model on a large Chinese hospital in Jiangsu. The fitting MAPE is 2.48%, and the RMSE is 16463.69 in the training group. The test MAPE is 1.91%, and the RMSE is 9354.93 in the test group. The results of both groups are better than those of the comparative models.

The two-stage hybrid grey model can solve traditional hospitals' seasonal outpatient volume forecasting and provide future policy formulation references for sudden large-scale epidemics.

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.

The effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.

First, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.

The predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.

Crude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

This paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.

This paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.

The selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.

The model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.

In practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.

Based on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

The purpose of this paper is to propose a new grey prediction model, GOFHGM (1,1), which combines generalised fractal derivative and particle swarm optimisation algorithms. The aim is to address the limitations of traditional grey prediction models in order selection and improve prediction accuracy.

The paper introduces the concept of generalised fractal derivative and applies it to the order optimisation of grey prediction models. The particle swarm optimisation algorithm is also adopted to find the optimal combination of orders. Three cases are empirically studied to compare the performance of GOFHGM(1,1) with traditional grey prediction models.

The study finds that the GOFHGM(1,1) model outperforms traditional grey prediction models in terms of prediction accuracy. Evaluation indexes such as mean squared error (MSE) and mean absolute error (MAE) are used to evaluate the model.

The research study may have limitations in terms of the scope and generalisability of the findings. Further research is needed to explore the applicability of GOFHGM(1,1) in different fields and to improve the model’s performance.

The study contributes to the field by introducing a new grey prediction model that combines generalised fractal derivative and particle swarm optimisation algorithms. This integration enhances the accuracy and reliability of grey predictions and strengthens their applicability in various predictive applications.

The global population has been experiencing an unprecedentedly rapid demographic transition as the populations have been growing older in many countries during the current decades. The purpose of this study is to introduce a Grey Exponential Smoothing model (GESM)-based mechanism for analyzing population aging.

To analyze the aging population of Sri Lanka, initially, three major indicators were considered, i.e. total population, aged population and proportion of the aged population to reflect the aging status of a country. Based on the latest development of computational intelligence with Grey techniques, this study aims to develop a new analytical model for the analysis of the challenge of disabled and frail older people in an aging society.

The results suggested that a well-defined exponential trend has been seen for the population ages 65 and above, a total of a million) during 1960–2022; especially, the aging population ages 65 and above has been rising rapidly since 2008. This will increase to 24.8% in 2040 and represents the third highest percentage of elderly citizens living in an Asian country. By 2041, one in every four Sri Lankans is expected to be elderly.

The study proposed a GESM-based mechanism for analyzing the population aging in Sri Lanka based on the data from 1960 to 2022 and forecast the aging demands in the next five years from 2024 to 2028.

This study aims to enhance the prediction accuracy of hydroelectricity consumption in China, with a focus on addressing the challenges posed by complex and nonlinear characteristics of the data. A novel grey multivariate prediction model with structural optimization is proposed to overcome the limitations of existing grey forecasting methods.

This paper innovatively introduces fractional order and nonlinear parameter terms to develop a novel fractional multivariate grey prediction model based on the NSGM(1, N) model. The Particle Swarm Optimization algorithm is then utilized to compute the model’s hyperparameters. Subsequently, the proposed model is applied to forecast China’s hydroelectricity consumption and is compared with other models for analysis.

Theoretical derivation results demonstrate that the new model has good compatibility. Empirical results indicate that the FMGM(1, N, a) model outperforms other models in predicting the hydroelectricity consumption of China. This demonstrates the model’s effectiveness in handling complex and nonlinear data, emphasizing its practical applicability.

This paper introduces a scientific and efficient method for forecasting hydroelectricity consumption in China, particularly when confronted with complexity and nonlinearity. The predicted results can provide a solid support for China’s hydroelectricity resource development scheduling and planning.

The primary contribution of this paper is to propose a novel fractional multivariate grey prediction model that can handle nonlinear and complex series more effectively.

This paper addresses the challenges associated with forecasting electricity consumption using limited data without making prior assumptions on normality. The study aims to enhance the predictive performance of grey models by proposing a novel grey multivariate convolution model incorporating residual modification and residual genetic programming sign estimation.

The research begins by constructing a novel grey multivariate convolution model and demonstrates the utilization of genetic programming to enhance prediction accuracy by exploiting the signs of forecast residuals. Various statistical criteria are employed to assess the predictive performance of the proposed model. The validation process involves applying the model to real datasets spanning from 2001 to 2019 for forecasting annual electricity consumption in Cameroon.

The novel hybrid model outperforms both grey and non-grey models in forecasting annual electricity consumption. The model's performance is evaluated using MAE, MSD, RMSE, and R², yielding values of 0.014, 101.01, 10.05, and 99% respectively. Results from validation cases and real-world scenarios demonstrate the feasibility and effectiveness of the proposed model. The combination of genetic programming and grey convolution model offers a significant improvement over competing models. Notably, the dynamic adaptability of genetic programming enhances the model's accuracy by mimicking expert systems' knowledge and decision-making, allowing for the identification of subtle changes in electricity demand patterns.

This paper introduces a novel grey multivariate convolution model that incorporates residual modification and genetic programming sign estimation. The application of genetic programming to enhance prediction accuracy by leveraging forecast residuals represents a unique approach. The study showcases the superiority of the proposed model over existing grey and non-grey models, emphasizing its adaptability and expert-like ability to learn and refine forecasting rules dynamically. The potential extension of the model to other forecasting fields is also highlighted, indicating its versatility and applicability beyond electricity consumption prediction in Cameroon.

Considering the impact of the Free Trade Zone (FTZ) policy on forecasting the port cargo throughput, this paper constructs a fractional grey multivariate forecasting model to improve the prediction accuracy of port cargo throughput and realize the coordinated development of FTZ policymaking and port construction.

Considering the effects of data randomization, this paper proposes a novel self-adaptive grey multivariate prediction model, namely FDCGM(1,N). First, fractional-order accumulative generation operation (AGO) is introduced, which integrates the policy impact effect. Second, the heuristic grey wolf optimization (GWO) algorithm is used to determine the optimal nonlinear parameters. Finally, the novel model is then applied to port scale simulation and forecasting in Tianjin and Fujian where FTZs are situated and compared with three other grey models and two machine learning models.

In the Tianjin and Fujian cases, the new model outperforms the other comparison models, with the least mean absolute percentage error (MAPE) values of 6.07% and 4.16% in the simulation phase, and 6.70% and 1.63% in the forecasting phase, respectively. The results of the comparative analysis find that after the constitution of the FTZs, Tianjin’s port cargo throughput has shown a slow growth trend, and Fujian’s port cargo throughput has exhibited rapid growth. Further, the port cargo throughput of Tianjin and Fujian will maintain a growing trend in the next four years.

The new multivariable grey model can effectively reduce the impact of data randomness on forecasting. Meanwhile, FTZ policy has regional heterogeneity in port development, and the government can take different measures to improve the development of ports.

Under the background of FTZ policy, the new multivariable model can be used to achieve accurate prediction, which is conducive to determining the direction of port development and planning the port layout.

Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.