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A Novel Grey Multi-attribute Three-way Decision Model Under Risk Preferences Yu Qiao, Lirong Jian, Yong Liu, Xu Wang The Journal of Grey System    2025, 37 (1): 16-32.   Abstract （352）            Knowledge map    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.   Related Articles | Metrics

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Data-driven Dynamic Grey-Verhulst SEIRD Model for Public Health Emergencies Forecasting Shuhua Zhang, Ming Liu, Bingjun Li The Journal of Grey System    2025, 37 (1): 33-46.   Abstract （333）            Knowledge map    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.  Related Articles | Metrics

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The Greyness and Applications of Grey Set Xican Li, Li Li The Journal of Grey System    2024, 36 (6): 42-53.   Abstract （326）            Knowledge map    In order to quantitatively describe the grey properties of grey set, based on the possibility function of grey set, this paper discusses the expression method of the greyness of grey set and its applications. Firstly, the axiomatic definition and a method of calculating the greyness of grey set are given, and its rationality is analyzed through examples. Then, according to the principle of unity of opposites, the concept of whiteness of grey set is given, and the applications of greyness of grey set are analyzed. Finally, some examples are given to verify the validity of greyness of grey set and its application model. The results show that the axiomatic definition of greyness of grey set not only conforms to the grey immortal axiom, but also can quantitatively describes the dynamic evolution state of grey hazy set (grey set). The application examples show that the grey relational degree model and the grey decision model based on the greyness of grey set are feasible and effective. The research results not only enrich the theory of grey mathematics and grey system, but also provide a new method for grey relational analysis and grey decision.   Related Articles | Metrics

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Forecasting the Two-Stage Regional Population Ageing Structure by Employing Grey Compositional Model  Hui Li, Naiming Xie, Rafał Mierzwiak The Journal of Grey System    2025, 37 (1): 1-15.   Abstract （323）            Knowledge map    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.   Related Articles | Metrics

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Comparative Analysis of Grey Forecasting Models for Population Aging Prediction: A Case Study of Egypt's Demographic Evolution Islam Mahmoud Sharafeldin, Naiming Xie The Journal of Grey System    2025, 37 (1): 108-117.   Abstract （296）            Knowledge map    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. Related Articles | Metrics

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Remaining Useful Life Prediction of Lithium Battery Based on LSTM and Improved GM (1, N) Model Qinqin Shen, Yang Cao, Shuang Liang, Quan Shi The Journal of Grey System    2024, 36 (6): 79-93.   Abstract （291）            Knowledge map    In response to the difficulties of online obtaining enough direct performance parameters for lithium battery remaining useful life (RUL) prediction, a novel prediction method that combines the long short-term memory (LSTM) neural network and an improved GM(1, N) model is proposed in this paper. Firstly, two correlation analysis methods are used to obtain the health indicators that characterize the health status of the lithium battery. Then, the existing lithium battery dataset is used to train the LSTM model and predict the initial capacity of the same type lithium battery in operation. Finally, the initial capacity and corresponding indirect health indicators are substituted into an optimized damping accumulation discrete multi-variable convolution model, and accurate prediction of the entire life cycle of lithium battery is achieved through rolling technique. Experiments are conducted by using for lithium battery datasets from the Center for Advanced Life Cycle Engineering at the University of Maryland. The results show that the proposed model performs much better than the LSTM model and the conventional GM(1, N) model. In particular, the mean absolute percentage errors of the proposed method for predicting the RUL of four lithium batteries are less than 2.5%, the root mean square errors are about 0.02, and the mean absolute errors are only about 0.01.  Related Articles | Metrics

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A Novel Time-varying Non-homogeneous Discrete Grey Model and Its Application in Forecasting Solar Energy Generation in Total North America  Lin Xia, Yuhong Wang, Yuxuan Han, Ke Zhou, Youyang Ren, Yiyang Fu The Journal of Grey System    2025, 37 (1): 96-107.   Abstract （288）            Knowledge map    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.   Related Articles | Metrics

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A Novel Power-sum Time-varying Grey Prediction Model and Its Applications Kai Cai, Lianyi Liu, Sifeng Liu The Journal of Grey System    2025, 37 (1): 64-78.   Abstract （280）            Knowledge map    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.  Related Articles | Metrics

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Research on Grey Prediction of Regional Dual Energy Consumption Under Carbon Emission Constraints Yuhan Xie, Chuanmin Mi The Journal of Grey System    2025, 37 (1): 79-95.   Abstract （272）            Knowledge map    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. Related Articles | Metrics

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Research on Image Recognition of Wood Defects Using TGARG Based on Edge Detection and Characteristic Combination  Yanping Qin, Jun Zhang, Huaqiong Duo The Journal of Grey System    2025, 37 (1): 118-132.   Abstract （270）            Knowledge map    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.   Related Articles | Metrics

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Equipment Maintenance Reliability Based On Grey Relational Decision Optimization Model  Qiang Li, Shupin Chen, Shumiao Fang, Ailing Yan, Wenjie Dong The Journal of Grey System    2025, 37 (1): 133-144.   Abstract （270）            Knowledge map    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.  Related Articles | Metrics

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A Flexible Time Power Grey Fourier Model for Nonlinear Seasonal Time Series and Its Applications  Xiaomei Liu, Jiannan Zhu, Meina Gao The Journal of Grey System    2025, 37 (1): 47-63.   Abstract （226）            Knowledge map    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.   Related Articles | Metrics

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An Unbiased Grey Model Based on Euler Polynomial and Its Application in China's Primary Energy Production Shuliang Li, Ying Wang, Ruifeng Zheng, Wei Meng, Dajin Zeng The Journal of Grey System    2025, 37 (2): 1-15.   Abstract （216）            Knowledge map    A key property of grey prediction models is their unbiased nature, which focuses on eliminating discontinuity between differencing and differentiation during their construction. Meanwhile, an unbiased proof is required to ensure this property. In this paper, an unbiased EDGM(1,1) model incorporating Euler polynomials is constructed. Firstly, this model integrates Euler polynomials and a time disturbance parameter into the classical GM(1,1) model, enabling this EDGM(1,1) model to flexibly handle sequences with various data characteristics. Subsequently, the difference and its discrete forms are derived, and the latter is then solved using the least squares method and mathematical induction. Then the Particle Swarm Optimization (PSO) algorithm is implemented to improve the model's parameters. Secondly, the compatibility of the EDGM(1,1) model is demonstrated, and its unbiasedness towards three characteristic sequences is proven based on Cramer's rule. Finally, the performance of the EDGM(1,1) model is evaluated comprehensively against five competing models using three metrics: MAPE, RMSE, and R². The comparative analysis shows that the EDGM(1,1) model outshines other models in robustness and accuracy. Furthermore, the novel model is designed to forecast China's primary energy outputs, aiming to provide references for energy policies and decision-making.  Related Articles | Metrics

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GreyShot: Zeroshot and Privacy-preserving Recommender System by GM(1,1) Model  Hao Wang The Journal of Grey System    2025, 37 (2): 16-22.   Abstract （195）            Knowledge map    Every recommendation engineer needs to face the cold start problem when building his system. During the past decades, most scientists adopted transfer learning and meta learning to solve the problem. Although notable exceptions such as ZeroMat etc. have been invented in recent years, cold-start problem remains a challenging problem for many researchers. In this paper, we build a zeroshot and privacypreserving recommender system algorithm GreyShot using GM(1,1) model by taking advantage of the Poisson-Pareto property of the online rating data. Our approach relies on no input data and is effective in generating both accurate and fair results. In conclusion, zeroshot problem of recommender systems could be effectively solved by grey system methods such as GM(1,1).  Related Articles | Metrics

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Multivariate Forecasting of Seasonal Carbon Dioxide Emissions via a Discrete Grey Multivariate Forecasting Model with a New Information Priority Accumulation Operator Jianming Jiang, Yandong Ban, Ming Zhang, Chiwen Qu The Journal of Grey System    2024, 36 (6): 69-78.   Abstract （191）            Knowledge map    In this study, a more efficient Discrete Grey Multivariate Forecasting Model with A New Information Priority Accumulation Operation is proposed to depict the development trend of energy-related seasonal carbon dioxide emissions. The new information priority accumulation operation and an adaptive grey action quantity in the new model ensure excellent nonlinear fitting capabilities. The presence of the virtual variable allows the model to directly simulate seasonal fluctuations in seasonal carbon dioxide emissions without removing seasonal effects, showcasing the model's superiority. Therefore, the model can fit the nonlinear seasonal time series better. Experiments based on quarterly carbon dioxide emissions from energy consumption in the United States demonstrate the new method's optimal forecasting performance. Additionally, the optimization capability of each component in the new model is further validated by a more in-depth experiment. The effectiveness of this method in fitting seasonal carbon dioxide emissions is confirmed.   Related Articles | Metrics

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Single-period Static Seru Scheduling Problem with Grey Processing Time Rui Tao, Liangyan Tao, Naiming Xie The Journal of Grey System    2024, 36 (6): 13-26.   Abstract （186）            Knowledge map    With the increase in demand for personalized customization and small-batch production in the manufacturing industry, the seru production system has been widely applied as a flexible and efficient production model. This paper primarily investigates the singleperiod static seru scheduling problem. The uniqueness of this study lies in considering the uncertainty of product processing time within the seru production system. It introduces interval grey numbers to represent the processing time of individual products and establishes a mathematical model. Additionally, this paper summarizes the methods for comparing the magnitude of interval grey numbers from previous research and proposes a new method for interval grey number comparison. To solve the model, this paper presents an improved genetic algorithm (GA-NS) that incorporates a neighbourhood search strategy. In the numerical experiment section, we compare the results obtained using the traditional genetic algorithm (GA) and the GA-NS algorithm. The results indicate that the GA-NS algorithm outperforms the traditional genetic algorithm in terms of optimization effectiveness and can effectively address seru scheduling problems that consider the uncertainty of processing times. This study not only enriches the theoretical research of interval grey number comparison methods but also provides a new optimization algorithm for solving seru production scheduling problems with uncertain processing times, offering significant theoretical and practical application value.  Related Articles | Metrics

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Multivariate Fractional Grey Model for Port Throughput Prediction  Xinyu Wang, Xinquan Liu, Yingyi Huang, Che-Jung Chang, Jianhong Guo The Journal of Grey System    2025, 37 (2): 23-32.   Abstract （177）            Knowledge map    Accurate prediction of port throughput is critical for enhancing the precision of port construction decisions. However, identifying the factors influencing port throughput and constructing a robust predictive model remain significant challenges. To address this issue, this paper develops a modeling framework based on grey systems theory. First, grey relational analysis is employed to identify the relevant factors impacting changes in port throughput. These influencing factors are then utilized to construct a multivariate weighted fractional grey model for throughput prediction. To enhance the predictive capability of the grey model, this study establishes an error-based objective function to determine the model's fractional order, followed by corrections to the residual sequence using Long Short-Term Memory (LSTM) neural networks to improve prediction accuracy. To validate the effectiveness of the proposed method, empirical analysis is conducted using port throughput data from Guangxi Province, with comparisons made against four commonly used models. The experimental results demonstrate that the grey modeling framework proposed in this paper achieves high accuracy, with a 0.67% reduction in mean absolute percentage error (MAPE) outperforming alternative models. Furthermore, the model predicts a rapid growth trend in port throughput in Guangxi over the next three years, suggesting that expanding the utilization rate of existing port infrastructure and accelerating investments in capacity expansion are critical for meeting future demand. These results highlight the model's potential as a decision-support tool for strategic planning in the port and logistics sectors.  Related Articles | Metrics

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Research on the Optimization of Flatness Grey Prediction Control Based on CNN-BiLSTM Haixia Wang , Kunjie Li , Linsen Wang , Xiao Cheng The Journal of Grey System    2024, 36 (6): 54-68.   Abstract （175）            Knowledge map    In the production of non-ferrous metal plates, strips, and foils, the shape control system has nonlinear, multivariable, and time-delay characteristics, making it difficult to achieve satisfactory control results through conventional control methods. Based on the grey residual error and CNN-BiLSTM(Convolutional Neural Networks- Bidirectional Long Short-Term Memory) model, this paper proposes a predictive rolling optimization control algorithm for accurately predicting the tensile stress value of plate shapes between roll gaps. With the parallel computing capability and error compensation technology of CNN-BiLSTM network, the proposed algorithm overcomes the shortcomings of no feedback mechanism and inaccurate dynamic process prediction value in residual prediction. As a result, it obtains more accurate full-process prediction data in rolling and compensates for the inertia and lag characteristics of the plate shape control actuator through rolling optimization control. The prediction accuracy of the grey neural network combination algorithm is compared with that of various models such as grey prediction, BP, CNN, and LSTM. The prediction accuracy is increased by 7.46%, 6.28%, 17.85%, and 17.2%, respectively, and the dynamic control accuracy is improved by 30%. This proves the effectiveness of the proposed algorithm and provides a new avenue for shape control and real-time data prediction. Related Articles | Metrics

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Estimating the Thermoelectric Performance Parameters of High Entropy Materials by the Improved Residual Error Non-homogeneous Grey Model(1, 1) Cholho Pang , Sonil Jo , Yonsun O , Songhun Kwak The Journal of Grey System    2024, 36 (6): 1-12.   Abstract （154）            Knowledge map    In this paper, an improved residual error non-homogeneous grey model(1,1) was newly developed and estimated the thermoelectric performance parameters (ZT figure of merit) of the high entropy materials(HEMs) using this model. Firstly, by combining the nonhomogeneous grey model, residual error processing method and Markov model, the forecasting accuracy of the model was improved. Secondly, the forecasting accuracy of the proposed model was compared with other grey models in simulating ZT values of AgSnSbSe1.5Te1.5. The comparative results showed that the forecasting accuracy of the proposed model was the highest (MAPE value < 0.02). Thirdly, this model was used to predict ZT values of high entropy materials at the high temperatures. The simulation result showed that ZT value of increased rapidly over 750K and were higher than 1.0 above 950K, continued to increase over the whole temperature range in Bi0.9Li0.1Cu0.9Mn0.1SeO. Meanwhile, ZT reached 1.81 at 1000K in Sn0.555Ge0.15Pb0.07Mn0.275Te, and ZT value of the Sn0.5Pb0.5Ge0.5Te(MnTe)0.15 had a maximum value of 1.72 at 900K and after that, it decreased. The results indicate that the proposed model is effective in predicting ZT values of high entropy materials.   Related Articles | Metrics

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Research on Construction of a Novel Grey Clustering Model Based on Possibility Functions Considering Dynamic Contribution Degree and Its Application  Shuaishuai Geng, Zhaohan Hu, Jing Jia, Xiao Xu, Sandang Guo The Journal of Grey System    2025, 37 (2): 50-62.   Abstract （152）            Knowledge map    This paper evaluates the high-quality development of national central cities by proposing a novel grey clustering method for the comprehensive assessment of their developmental levels. This approach facilitates dynamic analysis of urban development status and contributes to the theoretical framework of grey evaluation methods, thereby providing a robust foundation for urban development decision-making. The proposed method addresses the limitations inherent in traditional grey possibility function clustering models, particularly their inadequacy for panel data analysis and their lack of dynamic measurement capabilities in evaluating indicator systems. The novel model incorporates time weighting by optimizing the weights of time point index attributes to derive time domain attribute weights. For panel data, observed values are integrated into a comprehensive evaluation framework, facilitating dimension reduction and the transformation of panel data into cross-sectional data. Subsequently, grey clustering analysis is applied to the cross-sectional data. The validity and feasibility of the proposed model in handling panel data are verified through an evaluation and analysis of the high-quality development of national central cities.  Related Articles | Metrics