Accurate forecasting of energy consumption is critical for addressing challenges in energy allocation, especially as renewable energy plays a pivotal role in the pursuit of carbon neutrality. Renewable energy consumption exhibits distinctive trends and seasonal fluctuations, which calls for more sophisticated modeling approaches to ensure predictive accuracy. This study proposes a hybrid forecasting framework that combines grey system model with Gaussian process-based residual uncertainty analysis and a rolling prediction mechanism. The grey model generates forecasts on segmented subsets of the time series, while Gaussian process regression (GPR) analyzes the residual uncertainty, under the rolling prediction mechanism. Furthermore, the particle swarm optimization (PSO) algorithm is implemented to optimize the nonlinear parameters of the grey system model. The proposed framework is tested on

renewable energy consumption data from both commercial and residential sectors in the United States. Its performance is rigorously evaluated and compared against nine other grey hybrid models across four performance metrics. Results demonstrate that the hybrid model incorporating the fractional-order nonhomogeneous discrete grey model (FNDGM) and GPR (FNDGM-GPR) consistently outperforms the competing models in terms of both forecasting accuracy and generalization capability

The growing importance of environmental awareness in consumer behavior makes understanding attitudes towards green products crucial. This research aims to provide a practical model to deal with uncertainties, ambiguities, and insufficient data in quantifying and analyzing consumer attitudes in the context of sustainable consumption. To achieve this, an innovative combined approach of the SERVQUAL model based on Dynamic Grey Relational Analysis (DGRA) was developed to transform subjective feedback into measurable grey numbers for evaluating the gap between consumers' expectations and perceptions. Considering population aging challenges, the attitudes of elderly consumers aged 60 to 75 were considered for the practical analysis of the proposed framework. Key findings revealed substantial negative gaps between expectations and perceptions across most quality dimensions, suggesting green product attributes often do not meet anticipated standards, especially regarding environmental features. The results highlight an urgent need for brands to elevate product quality and enhance transparency in order to align with the evolving values of green consumption. The study emphasizes the need for transparent and accurate marketing to address gaps in consumer perceptions, build trust, and foster sustainable consumption practices, contributing to global sustainable development efforts.

This study combines the grey model and the regression tree model using the stacking method to create a novel ensemble learning model, aiming to improve the predictive performance of a single grey model in scenarios with large datasets and strong nonlinearity. In this approach, Extreme Gradient Boosting is used to perform regression fitting on the prediction errors of the grey model, and the prediction results from the first two steps are taken as inputs for the new ensemble learning model. This method provides a high-precision solution to nonlinear problems involving large datasets. Additionally, the Particle Swarm Optimization algorithm is employed in the residual regression step to automatically optimize model hyperparameters, further enhancing predictive accuracy. To verify and evaluate the model’s predictive performance, the proposed ensemble learning model was applied to the prediction of China’s 𝐶𝑂2 emissions. Thirteen different grey models were integrated with Extreme Gradient Boosting for analysis and evaluation. The experimental results demonstrate that the newly proposed ensemble learning model achieves excellent predictive accuracy and effectiveness, showcasing great potential for practical forecasting applications. All XGBoost-Stacked Grey Model variants achieved a Mean Absolute Percentage Error (MAPE) of less than 8% on the test set, with the lowest MAPE reaching 4.9159%, and the predicted curve closely matching the

actual trend.

To objectively evaluate the differences in AI industrial policies across regions and enhance the uniqueness, rationality,

comprehensiveness, and scientific rigor of policy measures, this study conducts a comparative analysis based on textual data from national, Xi'an, Jinan, and Chengdu AI industrial policies (2017–2024). Employing text mining techniques for word frequency statistics, we construct a Policy Modeling Consistency (PMC) index model comprising 10 primary and 47 secondary variables, supplemented by a grey relational analysis model to quantitatively assess policy heterogeneity among the three cities. Key findings include: (1) Divergent approaches in incentive policies—Xi'an emphasizes financial support and technical guarantees, Jinan prioritizes policy frameworks, while Chengdu focuses on fiscal incentives. (2) All three cities align their policy priorities with the national "New Generation Artificial

Intelligence Development Strategy," while incorporating local characteristics. (3) Innovation and technology emerge as central themes across all regional policies. By integrating the PMC index model and grey relational analysis, this study systematically compares inter-regional policy heterogeneity and proposes actionable recommendations, including refining intellectual property laws and regulatory frameworks, optimizing talent cultivation systems, and fostering robust innovation ecosystems.

This study considers a non-homogeneous discrete grey forecasting model with arbitrary accumulation operators, abbreviated as NDGM(1,1,k,c), to discuss the gross regional product of Sichuan. Firstly, we provide the definition of an arbitrary accumulation operator, and discuss several particular cases including the integer-order accumulation operator, the new information priority accumulation operator, the fractional-order accumulation operator, the conformable fractional-order accumulation operator, the Hausdorff fractional-order accumulation operator, the damping accumulation operator, and the probabilistic accumulation operator. Secondly, the NDGM(1,1,k,c) model with arbitrary accumulation operators is systematically studied with the grey modelling technique, the least squares estimation method and the salp swarm optimization algorithm. The perturbation bounds of the new model are discussed by the matrix perturbation theory. Finally, the NDGM(1,1,k,c) model is applied to the gross regional product of counties (cities, districts) in Sichuan. With raw data from 2011 to 2022, we develop different grey models under 20 subcases for each county/city/district which show that the NDGM(1,1,k,c) model can obtain competitive results and be suitable for studying and analyzing Sichuan county economy.

Natural gas plays an important role in China's low-carbon energy development and transformation process due to its clean, low-carbon, stable, flexible, and economic characteristics. To accurately predict the quarterly production of natural gas in China, this paper proposes a novel seasonal grey prediction model with weighted fractional order accumulation operator. Firstly, based on the seasonal fluctuations of the raw data, the raw data is divided into four seasonal groups. Secondly, when an external disturbance affects the system, the classic average weakening buffer operator is used to weaken its effects. Then, a new weighted fractional order accumulation operator is created

by combining the new information accumulation generation operator and the fractional order accumulation generation operator. Finally, the new information accumulation parameters λ and the fractional-order cumulative generating operator parameter r, are optimized using the particle swarm optimization technique (PSO). The experimental results show that the new grey prediction model (DGGM(1,1,λ,r)and DGDGM(1,1,λ,r)) performs better than other models in predicting quarterly natural gas production of China. Finally, the two models are used to estimate China’s natural gas production in the next 3 years and put forward some relevant policy recommendations.

The grey model proposed in this paper optimizes the accumulation method of the traditional grey model, and flexibly adjusts the generation sequence through the two parameters introduced, so as to explore the internal law of the data information at a deeper level, and achieve the purpose of improving the model accuracy.

Manufacturing enterprises serve as the main implementers for the high-quality development of China's manufacturing industry. Accurately identifying the key elements that evaluate and influence high-quality development is a prerequisite for exploring the path of high-quality enterprise development. This paper defines the connotation of high-quality development of manufacturing enterprises from two dimensions, "state" and "process", and constructs the characteristic behavior sequence and related factor behavior sequence for high-quality development of manufacturing enterprises accordingly. Using the grey superiority analysis model, an empirical study was

conducted on 1017 manufacturing enterprises. The study found that: (1) The evaluation elements for high-quality development in different sub-sectors of the manufacturing industry exhibit significant industry-specific characteristics and internal laws. The overall evaluation indicators for the manufacturing industry cover four dimensions: management capability, innovation effectiveness, social effects, and operational benefits. Capital-intensive manufacturing industries focus on operational benefits and management capability; technology-intensive manufacturing industries take innovation effectiveness and social effects as their core; while labor-intensive

manufacturing industries emphasize management capability and social effects. (2) The distribution of key relevant factors in different manufacturing sub-sectors presents significant industry heterogeneity and certain regularity. The high-quality development of the overall manufacturing industry and labor-intensive industries is jointly driven by three-dimensional factors of resources, environment and benefits. The key factors of capital-intensive manufacturing are concentrated in resources and environment, while the factors of technology-intensive manufacturing focus on benefits and environment. In summary, theoretically, the indicator system constructed in this paper and the key elements of each sub-sector derived from empirical research provide a clear indicator framework for subsequent

scholars to study specific sub-sectors. At the practical level, the research findings offer useful management insights for managers and policymakers of manufacturing enterprises in China.

A grey clustering evaluation system for the selection of prescribed performance constraint functions in prescribed performance controllers based on interval grey number measurement is constructed. A comprehensive performance evaluation index system based on finite time convergence characteristics, convergence time, tracking accuracy, maximum anti-interference ability, and comprehensive energy consumption was constructed, and interval grey number was used as the index evaluation measure. The combination weighting method that can integrate the advantages of subjective and objective weighting methods was used to determine the index weights. A grey clustering evaluation method based on the mixed possibility function of center points is constructed for evaluating the comprehensive performance of the controlled system under various prescribed performance constraint functions. An example analysis of trajectory tracking prescribed performance control for a permanent magnet linear motor (PMLM), comparing and evaluating the influence of six prescribed performance constraint functions on the comprehensive performance of trajectory tracking error, verified the effectiveness of the designed evaluation system and the reliability of the evaluation results.