Population ageing is a significant and global concern, particularly pronounced in China, where rapid ageing growth has been observed. This growth is uneven across regions, presenting urgent challenges for local governments. Accurate forecast of regional ageing structure is vital for developing and adjusting population, social, and economic policies. To address this, based on the compositional data, population ageing is firstly delineated into two stages: the structure of the elderly and that of the disabled elderly, and a data collection and pre-processing framework based on this division is constructed. Then, a novel non-linear dynamic grey Markov compositional model is developed to tackle this two-stage issue. Finally, using this model, the ageing structure is predicted and studied in Jiangsu Province, China, as an illustrative case. Experimental results show that the ageing structure will be further “aged” and “disabled”, and moderate disability is the core component of the rise in the disabled elderly. These forecasts align with current trends in ageing and provide a quantitative basis for governmental policy-making and adjustments.  

To address multi-attribute decision making problems where attribute values are interval grey numbers with partial weight information known, this study considers decision-makers’ risk preferences and integrates three-way decision theory to propose a novel grey multiattribute three-way decision model under risk preferences. Initially, in grey information systems lacking category labels and decision attributes, this model incorporates risk preferences to convert interval grey number-based evaluation values into corresponding real numbers, thereby quantifying decision information under uncertain conditions. Subsequently, grey relational analysis is employed to objectively determine conditional probabilities, significantly reducing subjective bias in decision-making. Furthermore, the model analyzes the relationship between evaluation values and loss functions, deriving a relative loss function matrix in interval grey number form, thus enhancing data reference value and improving model reliability. Building on this, this study establishes multi-attribute threeway decision rules suitable for grey environments based on risk preferences and explores the related theories of the new model. Finally, the new model is applied to the supplier selection issue, and its effectiveness, superiority, and stability are verified from multiple perspectives through comparative and experimental analysis.  

Determining parameters in infectious disease dynamics models is crucial for simulating and predicting the development trends of public health emergencies. Utilizing real-time epidemic data and grey systems theory, our innovative approach bridges the Dynamic Grey Verhulst model and the SEIRD model, which respectively have advantages in short-term and long-term forecasting. The new model features a dynamically adjusting decision cycle to accommodate evolving epidemic data. We constructed a dynamic grey Verhulst model using the principle of metabolism, enabling it to dynamically update and iterate important parameters of infectious disease models. This results in accurate simulation and prediction of epidemic dynamics. Taking the SARS-CoV-2 Omicron outbreak in Shanghai, China, in the spring of 2022 as an example, the proposed Dynamic Grey-Verhulst SEIRD model (DGVM-SEIRD) provides a data-driven, high-sensitivity and high-precision method for predicting public health emergencies. Sensitivity tests also confirm the superiority of our model. Furthermore, validation with H1N1 influenza data from Beijing, the COVID-19 outbreak in Wuhan and SARSCoV-2 emergencies in the UK reinforces our model’s accuracy. This methodology provides a highly flexible and responsive analytical tool for public health emergency management, offering scientific support for formulating more effective epidemic prevention and control strategies and emergency responses. 

Grey Fourier model has been successfully applied in seasonal time series forecasting, but its performance in handling nonlinear seasonal time series may still require further improvement. To describe the nonlinear characteristics, a flexible time power grey Fourier model (TPGFM(1,1,N,r)) is proposed by introducing nonlinear time power terms to the grey action of grey Fourier model. The hyperparameters, the truncated Fourier order N and time power r are initially selected by the Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal parameters are determined by the hold-out method. To further improve the prediction accuracy for nonlinear time sequences, combination models based on the proposed grey model, statistical models and artificial intelligence models are designed. The variable weights are assigned by the inverse variance weighting method. Afterward, the results of the designed experiments based on numerical experiment verify the validity of the Fourier order and time power selection, illustrating the superior performances over benchmark models. Finally, the proposed model is applied for monthly PM2.5 forecasting and quarterly wind power generation forecasting, outperforming other benchmark models in prediction, including seasonal grey models, artificial intelligence models and statistical models. Moreover, the combination models, developed based on TPGFM(1,1,N,r) model, have achieved higher prediction accuracy.  

The purpose of this paper is to propose an improved power-sum accumulation time-varying grey model (PATGM) to enhance the ability to mine the heterogeneity of sparse data. Firstly, a novel power-sum accumulation grey generating operator is introduced to smooth the observed values according to data fluctuations, mitigating the model's ill-conditioned property. Secondly, a time-varying function is introduced as a parameter structure to the traditional model, providing the model with flexibility in complex systems modeling. Finally, based on the Dingo Optimization Algorithm, a hyperparameter calibration strategy for PATGM is provided. The power-sum accumulation grey generating operator can amplify or minimize the nonlinear characteristics of the observations, thus significantly improving the adaptivity of the grey modeling approach to fluctuating sequences. Meanwhile, the elastic-net regression method is employed to obtain a more reasonable and stable parameter structure. The hyperparameters are calculated using the Dingo optimization algorithm, which effectively controls the noise resistance and nonlinearity in the prediction system. PATGM solves the data smoothing processing and model structure selection problems of the traditional grey model. This new model is suitable for processing data prediction tasks with complex characteristics, especially provides an effective prediction method for complex engineering and system modeling. 

To enhance the modeling capability of the grey prediction model in the spatiotemporal domain, the paper proposes a novel spatiotemporal grey prediction model integrated with heterogeneous adjacency accumulation. Initially, an improved economic geographic gravity matrix is employed to characterize the spatial flow patterns of regional energy consumption, vividly illustrating the spatial interplay between non-adjacent provinces. Subsequently, a heterogeneous adjacent accumulation operator is incorporated to mirror regional discrepancies in energy consumption and bolster the robustness of the spatiotemporal prediction model. Ultimately, the novel prediction model is utilized to forecast the evolution of regional dual energy consumption within the constraints of carbon emissions. The findings of this research reveal the following: (1) By 2030, the total energy demand is projected to surge to 6.839 billion tons of standard coal, surpassing the predefined threshold of 6 billion tons. The prompt implementation of energy-saving strategies is paramount to expedite the attainment of carbon peaking. (2) Energy consumption intensity exhibits notable regional variability, with a spatially positive correlation in energy consumption intensity among regions. By 2030, it is anticipated that only 12 provinces, including Beijing, Guangdong, Shanghai, and Jiangsu, will attain the energy efficiency benchmarks of advanced developed countries.

Accurate forecasting of solar energy generation in total North America is crucial for effective energy planning and environmental protection. However, challenges arise from the limited and complex nature of the data. This paper introduces a novel Time-Varying Non-Homogeneous Discrete Grey Model (TVNDGM(1,1)) to address these challenges. The model introduces an anti-forgetting accumulated generating operator as the weight accumulation function to effectively prioritize new information. Additionally, it extends the homogeneous discrete grey model into a non-homogeneous format, enhancing model adaptability to various samples. Applying the Whale Optimization Algorithm in selecting non-structural parameters further improves accuracy. Case study results demonstrate that the model achieves fitting and test errors of 2.28% and 1.65%, respectively, outperforming seven other methods, thus indicating superior predictive accuracy and stability. Forecasts suggest that from 2024 to 2030, solar energy generation in total North America will continue to rise, with an average annual growth rate of 20.31%. This study enriches the theory of new information prioritization within grey forecasting methods and provides technological support for global energy planning and development.  

Population aging in developing nations presents complex demographic challenges that conventional forecasting approaches often struggle to address effectively, particularly when confronted with endogenous volatility in demographic structures and limited data availability. This study introduces an enhanced hybrid grey forecasting framework to predict population aging patterns in Egypt, incorporating advanced grey models to improve prediction accuracy and capture regional demographic variations. Using comprehensive demographic data from 2011-2023, we evaluate multiple grey forecasting models to identify optimal prediction methodologies for different population segments. Our findings reveal that the Grey Optimization Model with Interval Analysis (GOM_IA (1,1)) demonstrates superior predictive performance, achieving the lowest Mean Absolute Percentage Error for urban populations, rural and aged populations during the testing period. While, Unbiased GOM (1,1) model give the best performance for the total population prediction over the other grey models. The model projects significant regional variations in aging patterns, with urban areas experiencing accelerated aging rates compared to rural regions. This study makes several key contributions by it establishing a robust methodological framework for demographic forecasting in developing nations with limited data availability. As well as providing quantitative evidence of regional disparities in aging patterns across Egypt. Finally, offering a data-driven insights for policy formulation in healthcare infrastructure development and social service delivery. The findings have significant implications for resource allocation and policy planning in Egypt and other developing nations experiencing similar demographic transitions. Furthermore, our research demonstrated the effectiveness of grey forecasting models in capturing complex demographic patterns and supports evidence-based decision-making in addressing the challenges of population aging.

Wood defects affect the use value and commodity value of wood, so the research on effective recognition of wood defects has important practical significance. In this study, three types of wood defect images (live knots, cracks, and dead knots) were used as research objects. To investigate the impact of edge detection and characteristics combination on recognition rate, the recognition method based on threedimensional grey absolute relational grade (TGARG) is constructed and the recognition rates of different types of wood defects were compared under different edge detection and characteristics combinations. The results show that, based on TGARG, the recognition rate of live knots is the highest (0.76) under edge detection by Canny operator as well as characteristics combination of energy and homogeneity. The recognition rate of cracks is the highest (1.00) under edge detection by Roberts or Sobel operator as well as characteristics combination of contrast and correlation. The recognition rate of dead knots is the highest (0.90) under without edge detection as well as characteristics combination of correlation, energy and homogeneity. The research method and conclusion proposed in this study on the selection of wood defect recognition from a new perspective will contribute to the development of wood defect recognition.  

Aiming at the selection of maintenance strategy for equipment reliability, This article first proposed a evaluation index system for equipment maintenance reliability from three perspectives: equipment operation guarantee, equipment maintenance, and equipment daily management and gives the modeling steps and flow chart of the grey correlation decision model, Delphi method and analytic hierarchy process are used to combine qualitative and quantitative analysis methods to determine and optimize the weight of qualitative indicators. Then, combined with the actual data of coating equipment operation and maintenance in a semiconductor panel manufacturing industry, a grey correlation decision optimization model is constructed to calculate the effect vector, the ideal optimal effect vector and the grey comprehensive correlation degree of the decision scheme of each index. Finally, through the grey correlation analysis, the optimal strategy selection of Coating equipment maintenance reliability is realized. The research in this paper has practical guiding significance for coating equipment maintenance decision-making, improving coating equipment maintenance reliability and reducing equipment maintenance cost.