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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.  
    Abstract350)           
    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.  
    Abstract554)           
    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.  
    Abstract308)           
    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.  
    Abstract195)           
    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.  
    Abstract250)           
    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.  
    Abstract248)           
    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.  
    Abstract259)           
    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.  
    Abstract291)           
    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.  
    Abstract293)           
    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.  
    Abstract275)           
    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.  
    Abstract220)           
    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.  
    Abstract267)           
    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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    A Grey Multi-objective Model for Slot Secondary Allocation of Arrival and Departure Flights under Autonomous Cancellation 
    Kejia Chen, Zhenkun Chen
    The Journal of Grey System    2024, 36 (6): 27-41.  
    Abstract190)           
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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.  
    Abstract395)           
    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.  
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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.  
    Abstract291)           
    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.
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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.  
    Abstract282)           
    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.  
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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.  
    Abstract639)           
    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. 
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    Research on Supply-Need Precise Matching of Aid to Disadvantaged University Students Based on Grey Correlation Analysis 
    Hongqi Liu, Zhiwen Tang, Jie Xiao
    The Journal of Grey System    2024, 36 (6): 94-103.  
    Abstract195)           
    The purpose of this paper is to explore a new approach to solve the problem of optimizing the allocation of university aid resources, then propose a grey relational model of aid supply-need precise matching. The conceptual connotations of precise aid and the process of need-oriented aid supply-need precise matching have been introduced at first. Then using the basic idea of grey relational analysis, the definition of supply-need matching grey nearness relational grade is proposed, and the steps of aid supply-need precise matching grey relational model are given. Finally, the constructed model is used to explore the problem of matching decision-making between aid recipients and aid resources, and differentiated aid strategy that effectively meets the needs of students and efficiently utilizes aid resources is given. The validity and rationality of the model are verified. The research shows that the grey relational model of aid supplyneed precise matching can be used to describe the precise matching problem between aid recipients and aid programs. It enables the optimal allocation of aid resources and the maximum satisfaction of aid needs to promote the organic integration of poverty alleviation and talent development. It can provide the decision-making basis and methodological support for the university aid administration, and have certain practical value. The model adheres to the student need-oriented configuration of aid programs, and it can form a differentiated aid strategy that effectively meets the needs of students and efficiently utilizes aid resources. This study provides a new perspective and a new way to solve the optimal allocation problem of aid resources for university students. It can provide the decisionmaking basis and methodological support for the university aid administration. 
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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.  
    Abstract427)           
    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.  
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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.  
    Abstract690)           
    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.  
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