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Improved Fractional Order Single Optimization Parameter Grey Model Jiangtao Wei, Yonghong Wu The Journal of Grey System    2023, 35 (4): 154-171.   Abstract （245）            Knowledge map    Some grey prediction models suffer from outliers and overfitting, and their prediction performance can be improved. Based on the fractional grey model (FGM) and the fractional time delayed grey model (FTDGM), an improved fractional single optimization parameter grey model (IFSGM) is proposed in this paper. A timetranslation power term is used to reduce model overfitting. The data is pre-processed to reduce the influence of outliers based on data transformation in cumulants and summations. The convolutional computational formulation is used to perform the prediction and improve the prediction effect. The genetic optimization algorithm is used to optimize the order of the fractional cumulants, find the optimal value of the order, and improve the model fit and prediction effect. In 6 data sets, the IFSGM and the 7 grey models are compared and tested. The experimental results show that IFSGM achieves excellent prediction performance.  Related Articles | Metrics

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A Novel Logistic Multivariate Grey Prediction Model for Energy Consumption: A case study of China Coal  Sihao Chen, Yongshan Liu, Huiming Duan The Journal of Grey System    2023, 35 (4): 132-153.   Abstract （170）            Knowledge map    Coal consumption plays a pivotal role in the national economic growth, and the coal-based energy supply system as the main guarantee of China's energy is impossible to change in the short term. In order to ensure the security of China's energy supply, accurate coal consumption forecast can provide important theoretical basis for the development of scientific and effective energy planning and decision-making. Starting from the classical Logistic model, this paper introduces a variety of related factors such as energy consumption, economic growth rate and carbon dioxide emission growth rate to expand the modeling objects of the Logistic model and improve the performance of the model by relying on its ability to capture the historical trend of the data model and accurately predict the future value. At the same time, a new logistic multivariate grey prediction model of energy consumption is established by introducing the principle of grey variance information organically combined with the logistic model. The modeling steps of the model are obtained by using mathematical methods such as least squares estimation of parameters and number multiplication transformation. Finally, the new model is applied to the prediction of Chinese coal consumption, and the validity of the model is verified from different perspectives of three cases, showing that the fitted and predicted data of the new model have good consistency with the actual results. The new model has a high accuracy for China's coal short-term forecast, and uses simulation and prediction effects of 1.68220% and 1.29866%, respectively, to effectively forecast China's coal consumption in 2022-2026, and points out the development trend of Chinese coal consumption, and provides a basis for China to make scientific and effective energy planning and decision-making. Related Articles | Metrics

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A New Optimized Grey Forecasting Model with Polynomial Term and Its Application An Wang, Yaoguo Dang, Junjie Wang The Journal of Grey System    2024, 36 (3): 74-85.   Abstract （141）            Knowledge map    China’s total energy consumption and production rank first in the world. However, China’s energy structure is not reasonable. Therefore, accurate prediction of future energy trends is of great significance for the Chinese government to adjust the energy structure. In this paper, we propose an optimized Grey Euler model with polynomial term, which is abbreviated as OSGEM(1,1,N), to forecast the total energy consumption and production of China in comparison with the commonly used prediction models. The data from 2002 to 2018 are used to simulate the parameters in the proposed model, and the data from 2019 to 2021 are used to test the improved approach. The results show that the OSGEM(1,1,N) model outperforms the other models. Finally, the OSGEM(1,1,N) model is used to forecast the total energy consumption of China from 2022 to 2025 and different results from the previous research results have been obtained.   Related Articles | Metrics

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Modeling and Predicting the Socio-Economic Performance of Countries Using Grey Relational Analysis and K-NN Algorithm Hande Hakan, Ecem Coşar Canlıer, Çiğdem Özarı, Esin Nesrin Can The Journal of Grey System    2024, 36 (1): 4-15.   Abstract （136）            Knowledge map    The main purpose of this study is to forecast the countries’ socio-economic performance with the fewest possible parameters. To do this, we propose a model consisting of methods from Multi-Criteria Decision Making and Machine Learning. Since the existence of different classifications of countries and several socioeconomic parameters, it becomes difficult to make a prediction of their belonging group and compare countries based on these parameters. Using the Grey Relational Analysis and the Critic method, we classify the countries into four different subgroups based on several socio-economic dimensions. K-Nearest Neighbor (K-NN) algorithm with basic macro-economic parameters is implemented to predict the countries' socioeconomic groups. The results rank the countries according to their socio-economic performance and predict the countries’ development levels for the future. The main findings indicated that the proposed approach can be used for similar research questions. The highest prediction percentages are accurate for small values of k. This study provides a convenient and effective method for grouping countries at different levels of development using basic economic parameters and provides a simple and practical method to predict the belonging group.   Related Articles | Metrics

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A Conformable Fractional Non-homogeneous Grey Forecasting Model with Adjustable Parameters CFNGMA(1,1,k,c) and its Application  Wenqing Wu , Xin Ma , Bo Zeng , Peng Zhang The Journal of Grey System    2024, 36 (2): 1-12.   Abstract （121）            Knowledge map    The inconsistency between the whitening differential equation and the grey basic form of the non-homogeneous continuous grey model CFNGM(1,1,k,c) will result in internal errors. Thus this paper proposes a CFNGMA(1,1,k,c) model with adjustable parameters, which improves the accuracy of the CFNGM(1,1,k,c). This paper first elucidates reasons for the internal errors generated by the continuous grey model CFNGM(1,1,k,c), and explains the classic method, the discrete grey forecasting model, of eliminating internal errors. On the basis of an in-depth analysis of the modeling mechanism of CFNGM(1,1,k,c) model, a new parameter adjustable grey forecasting model is proposed by introducing parameter adjustment factors to modify model’s parameters. Finally, the new model is applied to explore the gross regional product of Chengdu and Deyang in the Chengdu metropolitan area. The calculation results indicate that the newly proposed model can obtain more accurate results.  Related Articles | Metrics

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An Optimized Multivariate Grey Bernoulli Model for Forecasting Fossil Energy Consumption in China   Ye Li , Dongyu Liu, Meidan Xiao, Bin Liu The Journal of Grey System    2024, 36 (2): 67-78.   Abstract （117）            Knowledge map    Given the increasing severity of energy shortages, the exploration of effective strategies to optimize energy structures has become imperative. This requires careful consideration of energy consumption patterns, especially since these data are fundamental inputs for policy formulation. Given the uncertainty in the rate of change in energy consumption, this paper proposes an optimized multivariable grey Bernoulli model that is rooted in the grey Bernoulli model and incorporates background values and genetic algorithms. The grey Bernoulli model effectively linearizes nonlinear problems, thus simplifying computational procedures. In addition, to account for random fluctuations of relevant factors that may affect the model's predictions, this model introduces nonlinear correction terms that allow simulation and prediction values to adhere to the grey index law. The incorporation of background values enhances the model's ability to process information, providing it with a superior grasp of real data. Genetic algorithms can be used to refine the model's parameters, increasing its adaptability and precision. Finally, this paper applies the refined model to examine China's energy consumption patterns, validating its efficacy and versatility. Furthermore, energy consumption patterns for the next four years are forecast, with the analysis revealing that the growth rate of energy consumption from 2021 to 2024 shows a downward trend, particularly notable in 2024, where the growth rate is 1.64%.  Related Articles | Metrics

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Some Properties of Generalized Whiteness of Interval Grey Number Li Li, Xican Li The Journal of Grey System    2024, 36 (3): 25-36.   Abstract （114）            Knowledge map    In order to mine the intrinsic information of interval grey number, the concept of the generalized whiteness of interval grey number is first given in this paper based on the generalized greyness of interval grey number. Then the static and dynamic properties of generalized whiteness on bounded background domain, infinite background domain and infinitesimal background domain are analyzed, and the concepts of the extreme white system and extreme white spot are given. Finally, the conservation law of the generalized whiteness of interval grey numbers is given, and the generalized whiteness is applied to the ranking of interval grey numbers. The results show that the generalized whiteness of interval grey number on the bounded background domain has the static properties of the relativity, normality, unity, opposition, connectivity, justice and graduality; while on the infinite background domain and the infinitesimal background domain, the generalized whiteness of interval grey number has the above static properties except the graduality. On the bounded background domain, the generalized whiteness changes with the expansion of the background domain and the value domain, while on the infinite background domain and the infinitesimal background domain, the static and dynamic properties of the generalized whiteness of interval grey number are the same, it is not affected by the expansion change of the background domain and value domain, and the generalized whiteness of interval grey numbers is conserved. The research results not only enrich the grey system theory, but also provide a theoretical basis for the analysis and utilization of interval grey numbers. Related Articles | Metrics

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Exploring Death Population Prediction and Cemetery Planning in Chongqing amid an Aging Population: A Grey Forecast Model Based on Interval Grey Number  Huaan Wu, Yuhua Jin, Yinhe Xue, Bo Zeng, Hui Wang The Journal of Grey System    2024, 36 (3): 51-62.   Abstract （113）            Knowledge map    China’s population is steadily aging, contributing to the increase in the number of deceased people and the growing disparity between supply and demand for cemeteries. To provide theoretical support and data reference for cemetery planning, this study considers Chongqing, a city with a high rate of aging population, as an example to apply the interval grey number model to model and predict the size of the death population in Chongqing. The following conclusions are drawn: (1) The accuracy of the interval grey number prediction model in simulating the size of the death population in Chongqing exceeds 98%, indicating that the model employed in the study is suitable for medium- to long-term prediction; (2) The prediction results show that the annual death scale of registered population in Chongqing will range between 220 and 330 thousand from 2022 to 2030, with a fluctuating upward trend; (3) According to the size of the death population predicted, the cemetery market in Chongqing will experience a shortage of supply within 10 years. Therefore, in order to ensure a balance between the supply and demand of cemeteries in Chongqing, the government should actively promote the concept of green funerals and reduce the demand for cemeteries. Alternatively, it is also necessary to accelerate the planning and construction of cemeteries to avoid the predicament of people wanting to be buried without a tomb.   Related Articles | Metrics

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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.   Abstract （109）            Knowledge map    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.   Related Articles | Metrics

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Memorabilia of the Establishment and Development of Grey System Theory  Sifeng Liu, Liangyan Tao, Wei Tang The Journal of Grey System    2024, 36 (1): 1-3.   Abstract （106）            Knowledge map    This article summarizes and records important historical events in the establishment and 40 year development process of continuing innovation and dissemination of grey system theory, providing reference for scholars who pay attention to the evolution laws of grey system theory, a new branch of uncertainty system research, as well as colleagues engaged in grey system theory research. If there are any important omissions, we sincerely welcome readers to supplement and improve.  Related Articles | Metrics

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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.   Abstract （103）            Knowledge map    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.   Related Articles | Metrics

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Adaptive Fluctuation Grey Model withAK Fractional Derivative for Short-term Traffic Flow Prediction Quntao Fu, Shuhua Mao The Journal of Grey System    2023, 35 (4): 108-131.   Abstract （93）            Knowledge map    Short-term traffic flow prediction is an essential component of intelligent transportation systems. Shallow and deep pattern learning methods have been widely applied to short-term traffic flow prediction. However, shallow learning methods struggle with highly volatile data and models are usually constant-coefficient. On the other hand, deep learning methods require significant computational resources and time. In this paper, we propose a new adaptive fluctuation grey model for short-term traffic flow prediction. We combine the fractional differential equation and fractional accumulation generation operator, and expand the GM(1,1) model using trigonometric functions. Furthermore, we improve the Harris hawks algorithm by optimizing the distribution of the initial population with Cauchy mutation operator and introducing boundary constraint handling techniques to enhance the model parameter search capability. Finally, we apply the model to short-term traffic flow parameter prediction and compare it with the benchmark model. Results indicate that the new model shows better accuracy performance and better extraction of fluctuation information.  Related Articles | Metrics

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A Multi-attribute Decision-making Method Based on Grey Correlation Lirong Sun, Chi Zheng, Chenkai Jiang, Yinghua Tian, Yujing Ye The Journal of Grey System    2023, 35 (4): 76-90.   Abstract （93）            Knowledge map    Aiming at the grey feature problem of ' small sample and poor information ', this paper extends the traditional analytic hierarchy process, entropy method and ' vertical and horizontal ' scatter degree method to the field of grey number, and proposes a multi-attribute decision-making method based on grey correlation. Firstly, the applicable form of index weight is enriched, and the determination method of index weight in grey number form is given systematically. Secondly, aiming at the problem that the traditional evaluation method can not be directly applied to the comprehensive evaluation with grey characteristics, a comprehensive evaluation model in the form of grey number is proposed. Finally, through the interval grey number integration method and the ' kernel and grey number ' integration method, the evaluation values under each index are formed into a comprehensive evaluation value, and the evaluation results are sorted. Compared with the traditional evaluation method, the proposed method more reflects the rationality and dynamics of the evaluation results. Related Articles | Metrics

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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 （89）            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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Stock Movement Prediction With Sentiment Analysis Based on Grey Exponential Smoothing Method: A Case Study on Colombo Stock Exchange, Sri Lanka D.M. K. N. Seneviratna , M.V.D.H.P Malawana , R. M. K. T. Rathnayaka The Journal of Grey System    2023, 35 (4): 1-18.   Abstract （85）            Knowledge map    Sentiment  Analysis  is  an  innovative  development  technique  that  uses  natural language processing techniques to derive people's emotions under positive, negative,and neutral based on public opinions of information. The main objective of this study is  to  introduce  a  novel  stock  market  prediction  method  based  on  the  Grey Exponential Smoothing method for analyzing social media data within a big-data distributed environment. The empirical investigation of this study is mainly carried out based on the stock market price indices parallel to the extracted Tweets collected during the three selected politically important moments that happened in Sri Lanka during the past ten years; the first case study is based on the political background after  the  ending  of  the  thirty  years  of  civil  war  in  years  2009.  In  the  year  2015,Maithripala Sirisena ended the dynastic rule of Mahinda Rajapaksa. So, the second case  study  has  based  the Tweets  on  the  political  reforms  done  after  the  2015 presidential  election;  the  third  study  is  based  on  the  Sri  Lankan  political  and economic  background  after  the  Rajapaksas  rose  again  in  2020.  For  validations purpose, K Nearest Neighbour, Decision Tree Model, Support Vector Machine, Grey Exponential Smoothing model, and Multinomial Naïve Bayes machine learning were considered.  According  to  the  empirical  findings,  the  new  proposed  Hybrid  Grey Exponential Smoothing model is highly accurate with the lowest RMSE error values in one-head forecasting. Furthermore, the key finding of this research suggested that the  hybrid  Grey  Exponential  Smoothing  model  performs  well  in  sentiment classification-based financial predictions than traditional methods, especially with non-stationary behavioral backgrounds.  Related Articles | Metrics

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Ordinal Multivariate Grey Incidence Model and Its Application on Early Warning of Construction Quality Risk  Ke Zhang, Min Ma, Feizhen Zhang, Yuxin Zhou, Chunyong She, Zheng Zhang The Journal of Grey System    2024, 36 (3): 1-10.   Abstract （82）            Knowledge map    Government supervision is the highest level of construction quality management system. Due to a large number of constructions in progress, timely and accurate risk early warning is imperative for improving the efficiency of supervision. Aiming at the small-scale, ordinal, and unequal length multivariate time series of government supervision data, this paper proposes a construction quality risk early warning method based on ordinal multivariate grey incidence analysis. Firstly, to measure the dynamic similarity between risk indicators of projects, the proximity grey incidence model based on ordinal dynamic time warping (DTW) and the similarity grey incidence model based on ordinal L1 norm DTW are constructed respectively. Then, the two models are integrated to construct a comprehensive similarity model for construction quality risk warning. Combining the comprehensive similarity and k-nearest neighbour (k-NN) algorithm, a method of construction quality risk level classification and early warning is constructed. Finally, the method is applied to the quality supervision of water conservancy and hydropower projects in Zhejiang Province, and the results show that the proposed method can effectively solve the problem of construction quality risk early warning based on small-scale and ordinal data. Related Articles | Metrics

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Interaction-based nonlinear INDGM(1,N) model and its application Ye Li, Dongyu Liu, Junjuan Liu, Meidan Xiao The Journal of Grey System    2024, 36 (1): 56-62.   Abstract （81）            Knowledge map    Multivariate grey models are commonly used to evaluate the independent effects of related factors, but they may fail to account for any nonlinear interactions that could exist between them. To address this limitation, this study introduces the INDGM(1,N) model, which considers the nonlinear interactions between related factors. Simultaneously, to depict the nonlinear impact of both the system behavior sequence and corresponding factor sequences more accurately, varying power parameters have been incorporated into the model proposed in this paper. Moreover, by adjusting the parameter values of the INDGM(1,N) model, it can be converted into several other models, such as the DGM(1,N) model, GM(1,N) model, DGM(1,1) model, or GM(1,1) model. This study uses a genetic algorithm to obtain the time response of the INDGM(1,N) model by solving its nonlinear characteristic parameters. We then use the model to simulate and forecast China's CO2 emissions and compare its performance with that of other models. The results show that the INDGM(1,N) model provides more accurate simulation and prediction accuracy than other models, highlighting its effectiveness.  Related Articles | Metrics

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Forecasting PM2.5 Concentration with a Novel Seasonal Discrete Multivariable Grey Model Incorporating Spatial Influencing Factors  Yuanping Ding, Yaoguo Dang, Junjie Wang, Qingyuan Xue The Journal of Grey System    2024, 36 (2): 37-53.   Abstract （80）            Knowledge map    Given that PM2.5 concentration is not only related to local pollutants, but also affected by long-distance transmission of PM2.5 in adjacent areas, the key to improving the prediction accuracy of PM2.5 concentration is to comprehensively consider the effect of local influencing factors and the transmission effect of PM2.5 in adjacent areas. For this purpose, a novel seasonal discrete multivariable grey prediction model, encompassing spatial influencing factors, has been established. Firstly, we analyze the mechanism of spatial influencing factors and the reasonableness of using PM2.5 concentration in adjacent areas as the spatial influencing factors. Secondly, based on the spatial agglomeration characteristics of PM2.5 concentration, the K − means clustering algorithm is used to cluster adjacent cities with similar PM2.5 concentration, then the comprehensive value of PM2.5 concentration in each city cluster is calculated by weighted average combination. On this basis, a driving term of spatial influencing factors and a cosine trigonometric function term are introduced into the novel model to characterize the effect of spatial influencing factors on PM2.5 concentration and the seasonal fluctuation of itself, respectively. More importantly, the Genetic Algorithm Toolbox is employed to optimally determine the emerging parameters of this model, and the time response function of the novel model is calculated by mathematical induction method. Lastly, the new model is deemed valid through testing its PM2.5 concentration predictions for the cities of Beijing, Tianjin, and Baoding in the Beijing-TianjinHebei region. Based on the original observations from 2018Q1 to 2023Q2, the novel model is built for PM2.5 concentration prediction in 2023Q3 to 2024Q2 for the three cities. The findings imply that the newly developed model outperforms its competitors significantly and has the potential to serve as a robust tool for predicting PM2.5 concentration. Related Articles | Metrics

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Supplier Risk Assessment Research Based on Improved QFD-GC Method with Choquet Integral Daao Wang, Huan Wang, Zhigeng Fang The Journal of Grey System    2024, 36 (1): 16-21.   Abstract （76）            Knowledge map    In the realm of production and manufacturing, a symbiotic relationship with suppliers underscores the significance of rigorous supplier risk assessment. To address this growing need, our approach comprises four essential stages. Firstly, we have pioneered the development of an interval grey number QFD platform, a pioneering tool designed to discern and prioritize pivotal quality risk factors. Secondly, the Choquet integral is skillfully employed to navigate the intricate web of risk events' interrelations, thereby deriving the essential weightings of these risk factors. Thirdly, a cutting-edge grey clustering evaluation model is meticulously crafted, integrating the weightings of the risk factors. This model, a cornerstone of our methodology, is instrumental in classifying suppliers based on their respective risk profiles, optimizing risk management strategies. Lastly, our method's practicality and effectiveness are unequivocally validated through a real-world numerical example, conclusively showcasing its value in the context of supplier risk management.  Related Articles | Metrics

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Evaluation of Care Service Quality for Disabled Elderly Individuals in the Community Based on the Prospect-Grey Target House Model   Yun Fan, Jun Liu, Shuli Yan, Na Zhang, Xiaojun Guo, Zhigeng Fang, Sifeng Liu The Journal of Grey System    2024, 36 (1): 22-31.   Abstract （76）            Knowledge map    Considering the varying levels of disability among elderly people, the capability layer → demand layer → service layer structure was decomposed step by step. This enabled us to establish a quality house model that forges an association matrix between care needs and care service attributes for disabled elderly individuals residing in the community. Considering the decision maker's expected grey target and irrational risk attitude towards care service attributes, the prospect-grey target house care service quality evaluation model for disabled elderly individuals in the community was constructed based on prospect theory and grey target decision-making. By evaluating the quality of care services for disabled elderly individuals in the community, the care service levels of different types of disabled elderly individuals and groups that require improvements in care services were identified.   Related Articles | Metrics