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Identification of Key Elements for High-Quality Development of Manufacturing Enterprises Based on Grey Superior Analysis Ruyun Zhang, Zixuan Li, Yimin Huang The Journal of Grey System    2025, 37 (5): 96-112.   Abstract （283）            Knowledge map    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. Related Articles | Metrics

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Grey BP Neural Network Combinatorial Model with Time-delay Causal Term and its Application Jing Ye, Luolan Zhang The Journal of Grey System    2025, 37 (4): 1-12.   Abstract （253）            Knowledge map    In order to enhance the precisions of grey prediction models, it is essential to address the univariate constraints of the traditional GM(1,1) model and consider the influences of data’s time delay and nonlinear mapping on system behavior. In this paper, based on the grey model with background value optimization, we propose a time-delay optimized grey BP neural network combinatorial model (BP-TDOGM(1,1)) by introducing a time-delay causal term and combining with the BP neural network. The mechanisms of time delay, nonlinear mapping and related factor sequences on system behaviour are discussed in detail. Furthermore, the modelling framework, parameter estimation methods and model resolution techniques are investigated with a view to enhancing the capture of data correlations. These endeavours are designed to extend the scope of application of neural networks in scenarios characterized by limited information and to markedly optimize the prediction accuracy of the grey forecast model. Ultimately, the proposed model's efficacy is validated through an example of forecasting China's power production. This example offers a novel approach to address the practical challenges posed by limited time-delay information. It also serves as a decision-making reference for China's power sector, ensuring the harmonious development of power supply and the economy. Related Articles | Metrics

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Tree-Stacked Grey Model for CO₂ emission Prediction in China Yiqi Yang, Xin Ma, Yaling Zhang, Qingping He The Journal of Grey System    2025, 37 (5): 42-58.   Abstract （253）            Knowledge map    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. Related Articles | Metrics

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A Multi-attribute Quantum Decision Model Based on Grey Relational Analysis Shuli Yan, Yang Hu, Yizhao Xu, Xiangyan Zeng The Journal of Grey System    2025, 37 (4): 43-53.   Abstract （246）            Knowledge map    Aiming at the interference problem between decision-makers in uncertain group decision making, this paper proposes a new interference angle measure method based on quantum-like Bayesian network (QLBN). Firstly, the grey relational degree is extended to the positive and negative range, and then the grey relational degree is calculated according to the sequential growth trend, and it is transformed into the interference value. In this framework, the weights of the decision-makers are set as the first layer of QLBN, where they are determined based on the similarity between the personal opinion and the leading decision-maker’s opinion, and the conditional probabilities are calculated by combining the attributes’ weights and evaluation values. Finally, the quantum probabilities of alternatives are obtained. The alternatives are ranked according to the quantum probabilities, and the robustness and validity of the model are verified by numerical example. The result shows that the interference angle calculation method based on grey relational degree has a good performance in decision-making scenarios with incomplete information, and significantly improves the robustness and applicability of the quantum decision model. Related Articles | Metrics

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A Novel Seasonal Grey Prediction Model with Weighted Fractional Order Accumulation Operator and Its Application in Natural Gas Production Forecasting Mengqi Wu, Mingli Hu The Journal of Grey System    2025, 37 (5): 85-95.   Abstract （210）            Knowledge map    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. Related Articles | Metrics

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Using Grey System Analysis Methods and Models to Achieve the Design and Optimization of Aviation Tire Rubber Formulations Sifeng Liu, Jize Wang, Shaolin Ma, Wei Tang The Journal of Grey System    2025, 37 (5): 1-10.   Abstract （201）            Knowledge map    This study analyzes the critical role of aircraft tire performance in ensuring flight safety and stability. Given that the formulation design of natural rubber composites for aircraft tires still heavily relies on long-term empirical accumulation—a process with considerable randomness—this paper proposes, for the first time, the use of China's original grey system analysis and modeling methods to bring scientific rigor to the formulation design and optimization process. The author also outlines a practical and executable workflow for the formulation design and optimization of natural rubber composites for aircraft tires, which can serve as a reference for relevant industries and rubber formulation researchers. Related Articles | Metrics

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An Improved Conformable Fractional Grey Multivariate Model and Its Application Qinqin Shen, Linyun Yang, Yang Cao The Journal of Grey System    2025, 37 (4): 79-90.   Abstract （173）            Knowledge map    The conformable fractional accumulation generating operator (CF-AGO) can effectively handle information differences and deeply explore the laws of information development. Nevertheless, the CF-AGO fails to satisfy the highly crucial new information priority (NIP) principle. In this paper, a novel conformable fractional accumulation generating operator (NCF-AGO), which meets the NIP principle under certain conditions, is introduced firstly. Then an improved conformable fractional grey multivariate model with variable NCF-AGO is constructed. Both linear and nonlinear correction terms are considered in the model structure to fit data sequences with different features. The quantum particle swarm optimization algorithm is adopted to obtain the optimal accumulation orders and the optimal power exponent of the nonlinear correction term. In order to avoid the situation where overfitting of the model leads to poor prediction results, the Tikhonov regularization method, which includes the conventional least squares method as a special case, is proposed solve the involved model parameters. Finally, a case study from bending strength of concrete is given to show the effectiveness of the proposed model and its advantages over the well-known GM(1,N) model and several existing grey multivariate models. Related Articles | Metrics

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A Novel Dynamic Grey SERVQUAL Approach to Quantifying Consumers’ Attitudes Towards Green Products Ehsan Javanmardi, Amirhossein Najafabadiha, Sadaf Javanmardi, Sifeng Liu The Journal of Grey System    2025, 37 (5): 25-41.   Abstract （170）            Knowledge map    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. Related Articles | Metrics

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AI Policies Heterogeneity Evaluation Based on Text-Grey Relational Analysis Fang Wang, Songyang Zhang, Weihong Zhang The Journal of Grey System    2025, 37 (5): 59-72.   Abstract （167）            Knowledge map    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. Related Articles | Metrics

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A Hybrid Gaussian Process Regression-based Grey Model and Its Applications Chenxin Feng, Xin Ma, Yiwu Hao, Tianzi Li The Journal of Grey System    2025, 37 (5): 11-24.   Abstract （145）            Knowledge map    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 Related Articles | Metrics

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A Hybrid Evaluation Approach for Personalized Learning Effects Based on EEG Data: Integrating Grey Correlation, BP Neural Network and Fuzzy Evaluation Lijuan Wei, Jinming Qiu The Journal of Grey System    2025, 37 (4): 91-105.   Abstract （142）            Knowledge map    With the advancement of educational informatization and personalized learning, scientific evaluation of learning outcomes has become crucial for educational quality assurance. This paper proposes a hybrid evaluation approach integrating grey correlation analysis, BP neural network, and fuzzy evaluation based on EEG data for assessing personalized learning effects. The method establishes objective evaluation indicators through EEG data analysis, enabling real-time monitoring and assessment of the learning process. By adopting a multi-model fusion strategy, the accuracy and reliability of the evaluation are enhanced. The evaluation framework encompasses data preprocessing, feature extraction, model fusion, and result validation. Empirical research in primary education demonstrates that this method achieves 89% consistency with expert evaluation, 85% accuracy in cross-validation, and a correlation coefficient of 0.82 with academic performance. Over an eight-week intervention period, students showed significant improvements: attention levels increased by 35%, learning efficiency improved by 40%, and assignment quality enhanced by 28%. The research findings provide a new paradigm for data-driven educational evaluation and make significant contributions to advancing scientific and personalized development in educational assessment. Related Articles | Metrics

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The Assessment of Barriers to Access eHealth Services for Elderly Persons with Disabilities Based on Hybrid Multi-Criteria Decision-Making Models Xinrui Fang, Muhammad Nawaz, Sifeng Liu, Weiliang Zhang, Sihua Hou The Journal of Grey System    2025, 37 (4): 106-118.   Abstract （137）            Knowledge map    Providing eHealth services to elderly individuals with disabilities has become a critical global issue, especially in Pakistan, where access to these services often presents significant barriers that need to be identified and explored to ensure equitable and effective healthcare delivery. Therefore, this study aimed to identify and rank the barriers to access eHealth services for Pakistani disabled elderly. A survey was conducted to collect primary data, and 322 elderly people with disabilities provided their consent about facing barriers to eHealth services. The questionnaire was based on technological, individual, relational, environmental, and organizational constructs. Multiple-criteria Decision-making (MCDM)-based Dynamic Grey Relational Analysis (DGRA) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) were applied to explore and rank the significant barriers. We found the barrier “fear and dislike of technology” to be the top-ranked barrier evaluated from both DGRA and TOPSIS techniques. The Kruskal-Wallis (KW) test was also performed to assess the significance of this barrier for the three age groups of disabled elderly and found no significant differences among their age groups when aged ≥ 60 years. In Pakistan, this study is the first to use the DGRA, TOPSIS, and KW tests to examine the rank and significance of barriers to access eHealth services for the disabled elderly. Related Articles | Metrics

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Grey Pattern Recognition Model Based on Generalized Greyness of Interval Grey Numbers Xican Li, Li Li The Journal of Grey System    2025, 37 (4): 66-78.   Abstract （135）            Knowledge map    In order to solve the pattern recognition problem that the index value and weight are both interval grey numbers, a multi-index grey pattern recognition model based on generalized greyness is established in this paper. Firstly, the basic concepts of grey pattern, universal grey pattern and grey pattern recognition are given, and the principle of maximum possibility degree and the possibility function of single index grey pattern are given. Secondly, two methods of multi-index grey pattern recognition are given, that is, the comprehensive possibility degree model and proximity degree model, and the simplified forms of proximity degree model are given. Finally, the grey pattern recognition model is applied to the high-quality development evaluation of 15 national agricultural science and technology parks in Shandong province of China to verify the validity of the model. The results show that the proposed grey pattern recognition model has the advantages of strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application examples show that the proposed grey pattern recognition model is feasible and effective. The research results not only enrich the theory of grey mathematics and grey system, but also provide a new way for grey pattern recognition in cases where the weights and index values are all interval grey numbers or the coexistence of interval grey number and real number. Related Articles | Metrics

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A New Information Priority Adaptive Nonlinear Grey Bernoulli Model and Its Application Sandang Guo, Jing Jia The Journal of Grey System    2025, 37 (4): 119-136.   Abstract （134）            Knowledge map    To address the issues of nonlinearity, time-varying characteristics and new information priority in processing complex data, this paper proposes a new information priority adaptive nonlinear grey Bernoulli model. By integrating the Bernoulli equation, the time power term and the new information priority accumulation operator, the proposed model fully utilizes the effective information within sparse sample, thereby enhancing the adaptability of grey prediction models to nonlinear and volatile time series. This model's hyperparameters are solved using the Particle Swarm Optimization algorithm, and the objective function is optimized. Meanwhile, a quantitative method is adopted to select the modeling sequence of the case study. In the prediction of China's high-tech industry output, the new model is compared with five benchmark models and subjected to robustness testing. The results indicate that the new model outperforms the comparison models in terms of prediction performance, and exhibits strong robustness. Furthermore, the future output value of China's high-tech industry is predicted. Related Articles | Metrics

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An Extended Conformable Fractional Stochastic Grey Model and its Analysis in System Prediction#br# Yang Yang, Di Zhang, Xiuqin Wang The Journal of Grey System    2025, 37 (6): 1-13.   Abstract （134）            Knowledge map    Grey models are widely researched for system modelling and analysis. Considering the complexity of practical problems, grey models with both fractional and stochastic calculus can be used for mining the changing trend of the system with certain interference and uncertainty. For the simple expression and easier calculation of conformable fractional calculus, the conformable fractional stochastic grey model is proposed and discussed. The proposed model includes both random and deterministic factors, which can utilize the excellent characteristics of fractional and stochastic grey models. Several examples are used to test the performance of the proposed model. As a broader category model, conformable fractional stochastic grey one can integrate and expand the existing model with better physical meaning. The results show that new model has good performances in model analysis and short-term prediction. More novel models and application could be achieved for data mining, complex physical problems modelling and prediction. Related Articles | Metrics

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Quantum Interference-grey Correlation (QGRA) Modelling of UAV Combat Effectiveness Assessment Na Zhang, Jiaqi Zhou, Zhaojun Mao, Ding Chen The Journal of Grey System    2025, 37 (4): 28-42.   Abstract （133）            Knowledge map    Combat effectiveness assessment plays a crucial role in modern military operations, and its effectiveness directly affects combat efficiency, resource allocation and decision support. Firstly, the phase angle in quantum interference theory is introduced as the interference adjustment factor of grey correlation model, in which the traditional combat indicator system is reconstructed and optimized. Secondly, the properties and theorems of the grey correlation model after the introduction of quantum interference are analysed, and based on the quantum entanglement characteristics of UAV combat, its combat effectiveness is quantitatively evaluated through the quantum interference-grey correlation model. Finally, the effectiveness of this study is illustrated by a case study of UAV cluster formation programme. The results of the study show that the index assessment method not only improves the accuracy of combat effectiveness assessment, but also provides powerful support for actual military decision-making, demonstrating a wide range of application potential and important practical value. Related Articles | Metrics

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Research on the Importance Evaluation of Large Aircraft Suppliers Based on Combined Grey Clustering and Complex Network Tianyi Zhu, Lirong Jian, Yayu Zhang The Journal of Grey System    2025, 37 (4): 54-65.   Abstract （120）            Knowledge map    The evaluation of large aircraft suppliers' importance is crucial for supplier management and project stability. A method combining grey clustering and complex network theory is proposed for evaluating the importance of aircraft suppliers. The collaborative development network for the aircraft is first constructed through the work breakdown structure. Four centrality indicators of supplier network nodes are then employed, and a grey clustering model based on center-point mixed possibility function is applied to classify the suppliers. Taking the C919 aircraft as a case study, 43 suppliers are categorized into three levels. The roles and relationships of suppliers at each level within the collaborative development network are analyzed. The effectiveness of the evaluation model is verified, providing management insights and strategic recommendations for optimizing supplier management for the aircraft manufacturer Related Articles | Metrics

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Time-Series Cobweb Grey Target Model for Evaluating Misalignment Risks Between Traditional Energy Phase-Out and New Energy Substitution Jiefang Wang, Aiping Li, Manman Zhang, Jiali Wei, Yiyong Zhao The Journal of Grey System    2025, 37 (4): 13-27.   Abstract （120）            Knowledge map    The traditional energy phase-out and new energy substitution are critical to achieving the dual-carbon goal. Effectively coordinating these processes is essential for ensuring China’s energy security and achieving long-term carbon reduction. First, a Multi-Level Perspective (MLP) analysis framework is developed to examine the process of the traditional energy phase-out and new energy substitution under the dual-carbon goal, focusing on the misalignment mechanisms and their types. Second, an indicator system for evaluating misalignment risks is established, incorporating four key dimensions: new energy substitution capacity, new energy substitution level, traditional energy phase-out level, and carbon emission reduction achievement. Furthermore, a time-series cobweb grey target model is developed to evaluate and forecast misalignment risks during China’s 14th and 15th Five-Year Plan periods, and risk identification criteria are proposed. Empirical results confirm the effectiveness of the time-series cobweb grey target model. Related Articles | Metrics

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Grey Cluster Evaluation of Prescribed Performance Function Based on Center Point Mixed Possibility Function Chunwu Yin, Pei Yi, Zilan Zhao The Journal of Grey System    2025, 37 (5): 129-136.   Abstract （108）            Knowledge map    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. Related Articles | Metrics

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A Novel Generalized Fractal Grey Model for Postgraduate Education Scale Forecasting Caixia Liu, Zhenguo Xu, Keyun Zhao, Wanli Xie The Journal of Grey System    2025, 37 (5): 113-128.   Abstract （92）            Knowledge map    Aiming at the problems of insufficient adaptability and limited prediction accuracy of traditional grey prediction model in the application of complex nonlinear system, we provide a novel generalized fractal grey model in this study. Firstly, we innovatively construct a new difference operator called fractal difference. Then, based on this operator, a generalized fractal grey prediction model with exponential kernel (GFGM) is proposed, and the hyper-parameters of GFGM are accurately solved by intelligent optimization model. The model is more adaptable and able to describe complex data patterns more accurately. Finally, we apply the model to the prediction of graduate education scale, and the experimental results show that the GFGM model demonstrates higher accuracy and superiority compared to other traditional models. This study provides an efficient and accurate new tool for predicting complex systems. Related Articles | Metrics