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Entropy-weighted TOPSIS Multi-attribute Decision-making Model and Its Applications Based on Generalized Greyness Li Zhang, Xican Li The Journal of Grey System    2024, 36 (5): 15-26.   Abstract （346）            Knowledge map    In order to solve the decision-making problem that the attributive values are internal grey numbers and the attributive weights are unknown, this paper try to construct an entropy-weighted TOPSIS model based on the generalized greyness of interval grey number from the perspectives of proximity and equilibrium. Firstly, the properties of greyness distance are analyzed and the simplified formula for computing greyness distance is given. Then, a method to determine entropy weight based on greyness distance is given, and an entropy weighted TOPSIS decision-making model is established. Finally, the constructed model is applied to selecting brackish water irrigation pattern of winter wheat in North China Plain, China, so to verify its feasibility and effectiveness. The results show that the model proposed in this paper not only fully utilizes the measurement information of interval grey numbers, but also overcomes the influence of subjective factors on weights, and provide a new method for decision-making of unknown attributive weights and attributive value with interval grey number, and the interval grey numbers coexist with the real numbers. The application examples show that the model proposed in this paper is feasible and valid.  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 （317）            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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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 （313）            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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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 （299）            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 （277）            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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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 （262）            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 （253）            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 （251）            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 （248）            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 （242）            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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Evaluation of Barriers to Disabled Elderly’s Access to eHealth in China Using Grey Relational Analysis Muhammad Nawaz, Sifeng Liu, Naiming Xie, Mohammed Atef, Muhammad Wasif Hanif The Journal of Grey System    2024, 36 (5): 1-14.   Abstract （224）            Knowledge map    This study aimed to identify and rank the barriers faced by disabled elderly in China while accessing eHealth primary care services. Primary data were collected from the disabled elderly based on technological, individual, relational, environmental, and organizational constructs. The Dynamic Grey Relational Analysis (DGRA) and Multiple-criteria Decision-making (MCDM) based TOPSIS techniques were used to identify and rank the barriers. We found that the most significant barrier was “aging limitation (reduction in hearing, sight, memory, and fine motor control)” in both (DGRA and MCDM) cases. The Kruskal-Wallis test was used to investigate the significance of this barrier in different age groups of disabled elderly. We found no significant differences among the three age groups of disabled elderly, which shows that the barrier “aging limitation (reduction in hearing, sight, memory, and fine motor control)” is the most significant barrier at each age group (when age ≥ 60) of disabled elderly. The average value of Grey Relational Grades (GRGaverage) and the sorting outcomes of the MCDM of the construct individual were higher than those of all other constructs. This study is the first of its kind to apply the DGRA, MCDM and KWT to expose the barriers while accessing eHealth services for the disabled elderly in China.   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 （211）            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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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 （206）            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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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 （193）            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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An Improved Grey Time Power Model for Forecasting the Ecological Environmental Water Consumption In the Upper Yangtze River Basin Rui Duan, Shuliang Li, Weizhe Sun, Wei Meng, Dajin Zeng, Kui Yu The Journal of Grey System    2024, 36 (5): 80-95.   Abstract （185）            Knowledge map    Scientific and accurate forecast of ecological environmental water consumption (EEWC) in the upper Yangtze River basin is of major prominence to the sustainable development of the basin and the formulation of eco-environmental protection policies. Firstly, a two parameter variable weight buffer operator is used to pre-processing the system shock behavior sequence. Then, an improved grey model IGM4(λ,γ,ta) with four background values is established, introducing power exponential terms and linear correction terms to characterize data series with mixed linear and nonlinear relationships. The particle swarm optimization (PSO) algorithm is employed to find optimal parameters. Additionally, the model’s effectiveness is evaluated by comparing the fitting values of models with other grey models. The final results demonstrate that the IGM4( λ,γ,ta) performs best with mean absolute percentage error only 0.0199%. Finally, model IGM4( λ,γ,ta) is utilized to predict the EEWC in the upper Yangtze River basin from 2023 to 2028. The reasonableness of the predicted results is analyzed, and related policy measures are put forward.  Related Articles | Metrics

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Seasonal Grey Forecasting Model Based on Damping Accumulation and Its Application Ye Li, Chengyun Wang, Qiwen Wei, Shi Yao The Journal of Grey System    2024, 36 (5): 27-42.   Abstract （181）            Knowledge map    A new damping nonlinear grey multivariate seasonal forecasting power model DAFGM(1,N, , ) is proposed to solve the problem of small sample forecasting with seasonal, nonlinear, and uncertain system behavior characteristic sequence. Firstly, the seasonal moving filter is used to eliminate the seasonal characteristics of the original series. Then, according to the principle of "new information priority ", the damping accumulation coefficient is introduced, the unknown factors which are difficult to collect are simulated by introducing dummy variables, and a new seasonal forecasting model is constructed. Finally, the model is used to forecast the quarterly wind power generation in China. The results show that the model has good practicability and effectiveness.   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 （179）            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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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 （173）            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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A Temperature Error Correction Method with the ARIMA–GM(1,1) Model Xin Feng, Juncheng Jiang, Ni Lei, Li Lei, Haibing Feng, Zhiquan Chen, Shu Li The Journal of Grey System    2024, 36 (5): 58-69.   Abstract （165）            Knowledge map    To address the problem of temperature errors in secondary instruments operating in high- and low-temperature environments, this paper proposed a temperature correction method based on the ARIMA–GM(1,1) model. First, a standard source was connected to a temperature secondary instrument placed in a high- and low-temperature circulation box. The errors between the measurements of the standard source and the secondary instrument could be calculated and obtained a set of error sequences. Second, the error sequences were used to establish an ARIMA model and obtained a set of predicted values. And the residual between the errors and the predicted values could be calculated. To improve the accuracy of the ARIMA model, a GM(1,1) residual correction model was established based on the residual sequences. Lastly, the ARIMA and the GM(1,1) models were combined to formulate an ARIMA–GM model that could perform error self-correction for the temperature secondary instrument. In application experiments, the model achieved smaller average relative errors than a traditional ARIMA and hybrid models. Finally, we developed the ARIMA–GM(1,1) model into a software and applied it to cases of actual detection.  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 （163）            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