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    Research on China's GDP Growth Forecast Based on Grey Machine Learning Model
    Tianxiang Yao, Xichun Liu
    The Journal of Grey System    2024, 36 (4): 1-13.  
    Abstract245)           
    Based on Keynesian macroeconomic theory, this paper introduces economic indicators with Chinese characteristics, and constructs a multivariate grey machine learning forecasting model (IGM (1, N, X1 (0) )-IPSO-LSTM) to predict China's GDP growth. Firstly, IGM (1, N) model is constructed by changing the background value construction method of GM (1, N) model and introducing grey action constant A which reflects the change from the grey differential equation to the difference equation. Secondly, due to the low frequency and small amount of GDP data, constructing a two-layer LSTM model to increase the model complexity, so that the data can be fully trained. In addition, this paper uses nonlinear descending function instead of w to construct Improved Particle Swarm Optimization algorithm (IPSO), and adds Genetic Algorithm (GA) to IPSO to reduce the risk of particles falling into the local optimal solution. Finally, using IPSO to find the optimal parameters of LSTM model to predict China's GDP growth. By comparing the prediction accuracy of IGM (1, N, X1 (0) )-IPSO-LSTM model with other benchmark models, the prediction result of IGM (1, N, X1 (0) )-IPSO-LSTM model is the best. It is predicted that China's GDP growth rate in 2024 is 5.18% and in 2025 is 5.12%. By analyzing the trend development of China's economic, it is found that the forecast results are consistent with the expected trend of macro economy, which increases the credibility of the forecast results.  
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    Maintenance Modeling and Grey Lease Pricing for a Series Manufacturing System with the Machines from Multiple Suppliers
    Yaping Li, Yuhong Cheng, Tangbin Xia, Zhen Chen, Naiming Xie, Ershun Pan
    The Journal of Grey System    2024, 36 (4): 14-25.  
    Abstract147)           
    Leasing is an important mode of service-oriented manufacturing where a manufacturer may lease machines from multiple suppliers to form a manufacturing system. While the suppliers provide machine maintenance, their individual interests may not be necessarily optimal to the system. Therefore, we propose a maintenance modeling and lease pricing (MMLP) framework to find the optimal maintenance policy for the system, and make a lease pricing scheme as an incentive mechanism to promote the realization of the cooperative maintenance among the suppliers. An optimization model is established to obtain a long-term maintenance policy by minimizing a cost rate function. And then, the grey lease pricing scheme based on the fair allocation of the benefits from the cooperation is suggested, with the marginal contribution of each supplier in the cooperation measured by the grey Shapley value method. Finally, a case study is used to show the application of the MMLP framework, presenting that the joining of the suppliers can make maintenance cost reduced and that the lease prices determined by using the grey Shapley value demonstrate the emergence and risk of the cooperation.
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    Hydrogen Load Demand Prediction in Unified Energy System Based on Grey Ridgelet Neural Network
    Dou Qin, Bin Zhao
    The Journal of Grey System    2024, 36 (4): 26-32.  
    Abstract143)           
    Hydrogen will play critical pole in industrial field, heating field and transportation field, which can achieve mutual conversion of different energies. Hydrogen load prediction demand is important for establishing unified energy system, a novel prediction model is established based on particle swarm algorithm (PSA) and grey Ridgelet neural network (GRNN) to improve medium and long term hydrogen load demand prediction accuracy. Firstly hydrogen load demand prediction model in unified energy system is established, which concludes hydrogen load demand prediction models in industrial field, heating field and transportation field, and then total hydrogen demand model is deduced. Secondly, model of GRNN is constructed based on grey system theory and Ridgelet neural network, analysis procedure of GRNN is established. Structure of GRNN is confirmed, and mathematical model is constructed. To enhance prediction effectiveness of GRNN, PSA is used to optimize parameters of GRNN. Finally hydrogen load demand data in a province is selected to carry out prediction simulation, results show that prediction error of proposed PSA-GRNN ranges from 1.88% to 3.02%, which is less than that of other three prediction models, and fit goodness of proposed PSA-GRNN ranges from 0.958 to 0.985, which is also less than that of other three prediction models. Therefore proposed PSA-GRNN has better prediction precision and efficiency, which can obtain better precision effect and applicability. Hydrogen load demand prediction results in heating field based on PSAGRNN are closer to real value than that based on other three prediction models, results show that proposed PSA-GRNN has better prediction accuracy that other three prediction models.  
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    Construction of Symbiosis System for Rural Industry Revitalization Based on Lotka-Volterra Model and Stability Strategy Study 
    Na Zhang, Shuting Shi, Zihao Li
    The Journal of Grey System    2024, 36 (4): 33-54.  
    Abstract164)           
    The symbiotic system of rural industrial revitalization comprises farming households, grassroots governments, and new rural collective economies as symbiotic units. The optimal symbiosis mode within this symbiotic system is reciprocal symbiosis. This study focuses on Yuhang District in Zhejiang Province, Yining County in Xinjiang Uygur Autonomous Region, and Wangcheng District in Hunan Province as research areas. Firstly, the grey Lotka-Volterra (GLV) model is employed to analyze the interaction within the current symbiotic system of rural industrial revitalization across these regions using data from 2019-2023. Secondly, this paper utilizes the GM(1,1) model to predict future data for these regions and analyze their future symbiosis. Subsequently, this paper examines the equilibrium point and stability of the symbiosis systems within these regions. Finally, based on an evolutionary game model approach, key factors influencing the evolution of a stable symbiosis system when satisfying and balancing interest demands among symbiotic units are explored. The findings reveal distinct characteristics within each subject's rural industrial revitalization symbiotic system. Government subsidies' intensity and cooperation benefits and costs primarily influence its evolution towards stability. 
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    Grey Information Relational Estimation Model of Soil Organic Matter Content Based on Hyperspectral data
    Hong Che, Xican Li, Guozhi Xu
    The Journal of Grey System    2024, 36 (4): 56-68.  
    Abstract224)           
    In order to overcome the uncertainty in hyperspectral estimation of soil organic matter content, this paper aim to establish a grey information relational estimation model of soil organic matter content based on hyperspectral data and grey information theory. Based on 76 samples in Zhangqiu District of Jinan City, Shandong province of China, the spectral data are first transformed by the nine methods such as square root, first order differentiation of the logarithm reciprocal, and so on, the correlation coefficient is calculated, and the estimation factors are selected by using the principle of great maximum correlation. Then, according to the principle of increasing information and taking maximum method, the spectral estimation factors of each sample are sorted from small to large, and the grey information sequence is formed, and the grey relational estimation model of soil organic matter content is constructed based on the information chain. Finally, the estimation results based on different information chains are fused twice, and compared with the commonly used estimation methods. The results of the method in this paper show that the average relative error of the 12 test samples is 5.576%, and the determination coefficient R2 is 0.934, and the estimation accuracy is higher than that of commonly used methods such as multiple linear regression, BP neural network and support vector machine. The results show that the grey information relational estimation model using hyperspectral data proposed in this paper is feasible and effective, and it provides a new way for hyperspectral estimation of soil organic matter and other soil properties.  
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    Prediction of Digital Economy Development Levels in Urban Cities Based on the GCSA-GM(1,N) Model
    Chengxuan Wu, Cheng Tian, Fang Wang, Wenxin Cheng
    The Journal of Grey System    2024, 36 (4): 69-77.  
    Abstract190)           
    Based on the digital economy index (DEI) and Technological Innovation, Industrial Structure, GDP and Openness to the Development Index data of 15 sub-provincial cities from 2017 to 2021, we construct a framework to predict the development potential of the urban digital economy and analyse the spatial evolution trend under the ‘small data’ scenario using geometric causal strength analysis GM(1,N) and the gravity center model. The empirical analysis reveals that,15 sub-provincial cities, at least one of the influencing factors has a causal relationship with the urban DEI that is greater than 0.5. The average forecast error of the GM(1,N) model based on causality strength in 15 sub-provincial cities is less than 1% in 2022. This reflects that four influencing factors can be used as an effective indicator to measure the level of digital economic development. The forecast results also indicate that the digital economy center of China’s sub-provincial cities will evolve from north to south and from east to west in 2022-2025. Finally, this study presents suggestions from three aspects: Strengthening technological innovation, promoting industrial digital transformation and upgrading, and strengthening cross-regional cooperation and exchanges.  
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    Residual Life Prediction of High-pressure Pipeline Erosion Based on the Grey Markov Model
    Liu Xiong, Mo Li
    The Journal of Grey System    2024, 36 (4): 78-89.  
    Abstract91)           
    Based on the digital economy index (DEI) and Technological Innovation, Industrial Structure, GDP and Openness to the Development Index data of 15 sub-provincial cities from 2017 to 2021, we construct a framework to predict the development potential of the urban digital economy and analyse the spatial evolution trend under the ‘small data’ scenario using geometric causal strength analysis GM(1,N) and the gravity center model. The empirical analysis reveals that,15 sub-provincial cities, at least one of the influencing factors has a causal relationship with the urban DEI that is greater than 0.5. The average forecast error of the GM(1,N) model based on causality strength in 15 sub-provincial cities is less than 1% in 2022. This reflects that four influencing factors can be used as an effective indicator to measure the level of digital economic development. The forecast results also indicate that the digital economy center of China’s sub-provincial cities will evolve from north to south and from east to west in 2022-2025. Finally, this study presents suggestions from three aspects: Strengthening technological innovation, promoting industrial digital transformation and upgrading, and strengthening cross-regional cooperation and exchanges.  
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    Assessing the Service Quality of Fisherman's Homestays in China: a Hybrid MADM Approach Consisting of DANP and Grey Clustering Evaluation
    Peng Jiang, Rui Chi, Hui Xia, Longyun Zhang, Chuandong Ju
    The Journal of Grey System    2024, 36 (4): 90-110.  
    Abstract152)           
    Nowadays, a new emerging tourism industry, named fisherman's homestay, has become a very representative marine leisure tourism project, widely promoted in coastal areas in China. However, the development of China's fisherman's homestay industry is not yet mature and there are many problems, such as incomplete laws and regulations, lack of infrastructure, and severe homogenization. Therefore, it is very important to help the owners of fisherman's homestay improve the service quality. Based on the Service Quality Gap Model, this paper establishes an evaluation index that affects the service quality of fishermen's homestay. We apply decisionmaking trial and evaluation laboratory-based analytic network process (DANP) to identify the critical factors and the causal relationship between them. And the grey clustering model is used to evaluate the service quality of Liaoning province and other five places. Experimental results reveal those six factors, including surrounding facilities, online marketing, room infrastructure, personalized service, community co-prosperity, and attention to harmonization with the environment, contribute to improving the service quality of fisherman's homestays. The fisherman's homestays in Shandong Province, Liaoning Province, and Zhejiang Province are in "excellent" level, and the fisherman's homestays in Fujian Province and Guangxi Zhuang Autonomous Region are in "good" level. 
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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.  
    Abstract191)           
    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.  
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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.  
    Abstract299)           
    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. 
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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.  
    Abstract148)           
    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.  
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    Novel Grey SIRS Model Forecasts Credit Risk with Nonlinear Infection
    Qian Lv, Xinping Xiao, Mingyun Gao
    The Journal of Grey System    2024, 36 (5): 43-57.  
    Abstract104)           
    Epidemic models are widely used in financial risk prediction. The problems of nonlinear changes in infection rates and limited data samples in financial risk remain to be addressed. To this end, this paper proposes a nonlinear grey SIRS (abbreviated as GSIRS) model based on short-term data. This model employs a time-varying function to capture the nonlinear dynamics of infection rates, and integrates the system grey prediction model to analyze short-term data. Parameter optimization is achieved through the least square method and the whale optimization algorithm. The GSIRS model shows good prediction accuracy across three financial crisis datasets, with MAPE ranging from 3.379% to 4.981% for training sets and 2.913% to 3.212% for test sets. These values are significantly better than those of competition models. In addition, the CWC values of the interval prediction under the 95% confidence level of the model are 0.13, 0.14 and 0.33, respectively. The combination of excellent RMSE and STD metrics further proves the stable forecasting ability. Meanwhile, the sensitivity analysis shows that changes of infection rate have a 1-2 period lagged effect on the infected individual density.  
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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.  
    Abstract139)           
    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. 
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    A New Grey Forecasting Model with Fractional Order Accumulation Generation Operation and Its Application in GDP Forecasting
    Qifeng Xu, Yongjun Guan , Yunbao Xu, Ran Wang
    The Journal of Grey System    2024, 36 (5): 70-79.  
    Abstract118)           
    In this paper, a new fractional-order grey forecasting model with a temporal power term that can handle both annual and quarterly forecasting tasks for GDP is presented. The model's characteristic is that it has a dynamic simulation parameter, which can automatically adjust the structure of the model according to the need of the prediction task to achieve the purpose of accurate prediction. In addition, the fractional order parameter and power term parameter of the model play an important role in enhancing the adaptive performance of the model. In particular, an excellent intelligent optimization algorithm, the Ant lion optimizer, is used to solve the model's programming model to obtain the hyperparameters for modeling quickly. In this study, China's annual GDP and quarterly GDP are used as research objects to verify the validity of the new model. The experimental results show that all evaluation indicators of the proposed method are better than those of its competitors. Therefore, the model has some application value. 
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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.  
    Abstract149)           
    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. 
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    Foreword (1) to Grey Systems Analysis: Methods, Models and Applications 2nd Edition
    E. K. Zavadskas
    The Journal of Grey System    2024, 36 (5): 106-106.  
    Abstract117)           
    As a new edition of Grey Systems Analysis by Professor Sifeng Liu is about to be published, I am great honored to write the preface for this classic work in the field of grey systems research. In the mid to late 20th century, human society began to move towards the information age.People are beginning to deeply realize that data analysis methods have become an indispensable skill for everyone.The characteristics and operating rules of various systems are like gold buried in a sea of sand, deeply concealed by the chaotic and complex data information, and there is an urgent need for effective scientific methods to explore and reveal.In response to the needs of the times, as a poverty information data analysis method, grey system theory has emerged. Grey system theory takes the "poor data" uncertain system with "some information known and some information unknown" as the research object. It mainly extracts valuable information through the mining of "some" known information, and realizes the correct description of the system operation behavior and evolution law, so that people can use mathematical models to analyze and assess the "poor data" uncertain system, then realize high-precision prediction, scientific decision-making and optimal control of the "poor data" uncertain system. Prof. Liu has been dedicated to grey system research for 40 years, and his series of original concepts and models have become classics in the field. Such as general grey numbers, simplified forms of grey numbers, and their algebraic systems; Construction and properties of sequence operators and practical buffer operators; A series of grey relational analysis models based on a global perspective; The grey evaluation model based on a mixed possibility function of endpoints and center points, a multiobjective weighted intelligent grey target decision-making model, and a two-stage grey decision-making model based on a kernel weight vector group; And various original poverty information data prediction models such as original difference models, mean difference models, discrete grey models, fractional order grey models, and self memory models proposed in collaboration with his students. Especially his seminal books, greatly promoted the dissemination and development of grey system theory. The Grey System Theory and Its Applications, first published in 1991, were deeply loved by readers. In 2024, Science Press released its 10th edition, which was rated as the first highly cited book in pandect of Natural Science by China National Knowledge Infrastructure. Multiple English versions, such as An Introduction to Grey System Theory(1998, IIGSS Academic Publisher, USA), Grey Information(2006, Springer London Ltd, UK), Grey Systems (2011, Springer-Verlag, DE), Grey Data Analysis (2016, Springer, SG), Grey Systems Analysis (2022, Springer, SG), are the first choice for scholars from all over the world to understand grey system theory and its research progress. Currently, scholars from over 130 countries or regions around the world have published papers on grey systems. My team has been conducting grey system theory research for over 20 years. And starting to publish papers related to grey systems in the early 21st century.We have successfully applied grey system methods and models to solve problems such as construction project evaluation and supplier selection, and proposed multiple combined grey models, such as COPRAS-G, ARAS-G, and EDAS-G, etc. This book will undoubtedly benefit more grey system theory learners and researchers as it is published in OA format with the support of the Excellent Academic Works Publishing Fund of Northwestern Polytechnical University. Grey system theory is a powerful tool for analyzing uncertain data in the era of big data. I look forward to its widespread dissemination worldwide, promoting the in-depth application of grey system theory in the fields of natural sciences, social sciences, and engineering technology.
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    Foreword (2) to Grey Systems Analysis: Methods, Models and Applications 2 nd Edition 
    Alain BERNARD
    The Journal of Grey System    2024, 36 (5): 107-107.  
    Abstract86)           
    In the era of big data, the paradigm of scientific research is undergoing fundamental changes. The Fourth Paradigm: DataIntensive Scientific Discovery which proposed by Jim Gray, a Turing Award winner, is increasingly becoming the mainstream paradigm in scientific research. The significant feature of big data is its low information density. The characteristics and operation rules of various systems are like gold buried in a sea of sand, deeply concealed by the big chaotic and complex uncertain data. In 1982, Professor Julong Deng founded the Grey System Theory, which is a distinctive method for modeling and analyzing uncertain data. Grey system theory takes the "poor data" uncertain system with "some information known and some information unknown" as the research object. It mainly extracts valuable information through the mining of "some" known information, and realizes the correct description of the system operation behavior and evolution law, so that people can use mathematical models to analyze and assess the "poor data" uncertain system, then realize high-precision prediction, scientific decision-making and optimal control of the "poor data" uncertain system. Prof. Liu has been dedicated to grey system research for 40 years. The series of concepts and models he proposed have become classics in this field. Such as kernel, degree of greyness of grey number, simplified form of grey number, general grey numbers and their algebraic systems; sequence operator, weakening and strengthening buffer operators; A series of grey relational analysis models based on a global perspective; The grey evaluation model based on mixed possibility function of endpoints and center points, a multi-objective weighted intelligent grey target decision-making model, and a two-stage grey decision-making model based on a kernel weight vector group; And various original poverty information data prediction models such as original difference models, mean difference models, discrete grey models, fractional order grey models, and self memory models proposed in collaboration with his students. These original achievements have greatly enriched the knowledge system of grey system theory. Various editions of his seminal book on Grey system theory have been published in different languages such as Chinese, English, Romanian and Korean. Hundreds of universities from around the world adopted them as textbooks. There are more than one million audiences of his books, videos and software of grey modeling. In 2024, he was selected as one of the top 0.05% Lifetime Highly Ranked Scholar in Systems Theory by Scholar GPS. His publications have been cited 51270 times with an H-Index of 95 in Huezhi Scholar. As a new edition of his book of Grey Systems Analysis is about to be published, I am great honored to write the foreword for this classic work. This book will undoubtedly benefit more grey system theory learners and researchers as it has been funded by Publishing Fund of Excellence Academic Works of NPU and will be published as OA book. It is expected that it will be widely spread around the world, promote the in-depth application of grey system methods and models, and benefit all mankind.  
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    An Optimization Scheme for Enhancing the Performance of Fractional-order Grey Prediction Models in Seasonal Forecasting Tasks: the Case of the Fractional-order GM(1,1) Model
    Yanan Li, Liang Zeng
    The Journal of Grey System    2024, 36 (5): 96-105.  
    Abstract105)           
    Fractional-order grey prediction models have gained wide recognition for their computational efficiency and straightforward modeling mechanisms. However, their performance in seasonal forecasting tasks still needs improvement. To address this, this paper designs a novel optimization scheme and applies it to the representative fractional-order grey GM(1,1) model (FGM(r,1)) to advance research in this area. In this optimization scheme, the dummy variable is used to enable the model to directly handle seasonal time series, the discretization technique is employed to simplify the computational steps, and the Bernoulli parameter and the linearly weighted hybrid fractional-order accumulation strategy are used to enhance the model's fitting capability. To verify the effectiveness of the proposed method, the optimized model and some benchmark algorithms are used to model three quarterly data sets. The experimental results show that the optimized model can produce better performance, which verifies the effectiveness of this optimization scheme. 
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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.  
    Abstract118)           
    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.  
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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.  
    Abstract129)           
    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. 
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