The Journal of Grey System

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1. Grey Relational Frame Prediction Method for Anomaly Detection

Chaobo Li, Hongjun Li, Xiaohu Sun, Guoan Zhang

The Journal of Grey System 2022, 34 (1): 1-16.

摘要（243）

Anomaly detection is a common problem in security and protection systems. Unlike conventional methods, considering the feature correlation and the uncertain predicted frames, a grey relational frame prediction method is proposed for the anomaly detection task. The future frame prediction network is designed by adversarial learning, consisting of generative and discriminant modules. In order to solve the lack of feature correlation, we integrate Deng’s grey relation into the generative module to calculate the correlation between the predicted features and previous features during training. Furthermore, the grey absolute relation is introduced to deal with the uncertainty of predicted future frames. This network is optimized with different loss functions that combine the adversary, grey relation, pixel, gradient, and optical flow. These losses can well measure the difference between the predicted future frames and real future frames in temporal, spatial, and feature aspects. Experiential results show the proposed method obtains the averaged AUC of 84.1%, 95.7%, 85.6% on UCSD Ped1, Ped2, and CUHK Avenue datasets, which are 1%, 0.3%, 0.5% higher than the network without grey relation analysis. Extensive experiments demonstrate the superiority of our model in anomaly detection.

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2. Multi-variable GMU(1,N) Grey Prediction Model Considering Unknown Factors

Ye Li, Yuanping Ding, Jianping Wang

The Journal of Grey System 2022, 34 (1): 17-33.

摘要（252）

The multi-variable grey prediction model represented by the GM(1,N) is an important casual relationship forecasting model. However, the traditional GM(1,N) model shows some defects which affect the modeling accuracy and applicability. In this paper, the modeling process of the traditional GM(1,N) model is studied, and three defects are observed in terms of “modeling mechanism,” “modeling structure,” and “parameter estimation.” To address these defects, a novel multi-variable GMU(1,N) grey prediction model considering unknown factors is proposed by introducing an exponential function \beta e^(\alpha(k-1)) in this paper, the modeling assumption in the traditional GM(1,N) model that \sum b_i X_i (k) can be treated as a grey constant with a small variation range of X_i (1) (i=2,3,……,N) is dropped, and the derivation form of the GMU(1,N) model is defined, which solve these three defects in the traditional GM(1,N) model effectively. Meanwhile, the genetic algorithm toolbox and recursive method are used to solve the parameter \alpha and time response function, respectively. Additionally, it is theoretically proved that the GMU(1,N) model can be completely compatible with the GM(1,1) model, GM(1,1,e^at) model, GM(1,N) model, and GMC(1,n) model by adjusting the parameters’ values. The GMU(1,N) model is used to simulate and predict grain production in Henan province to verify the effectiveness of these improvements. The mean average simulated and predicted relative errors of the GMU(1,N) model are 0.000% and 0.811%, in comparison with the traditional GM(1,1) model and the GM(1,N) model, which are 1.234%, 1.487% and 8.105%, 8.874% respectively. Results show that the GMU(1,N) model has superior performance, which confirms the effectiveness of the model improvement.

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3. Analyzing the Aging Population and Density Estimation of Nanjing by Using a Novel Grey Self-Memory Prediction Model Under Fractional-Order Accumulation

Xiaojun Guo, Jiaxin Li, Sifeng Liu, Naiming Xie, Yingjie Yang and Hui Zhang

The Journal of Grey System 2022, 34 (1): 34-52.

摘要（294）

At present, China's aging population is becoming increasingly prominent. Accurately predicting the number and density distribution of the elderly population in the future is conducive to accelerating the development of aged care services and has important reference value for formulating relevant policies and social development. In this paper, a novel SM-FGM model is constructed to predict the quantity and density distribution of the elderly population in Nanjing from 2021 to 2030. The combined model combines the advantages of fractional-order accumulation and self-memory algorithm and has good prediction accuracy and generalization ability. Fractional-order accumulation can effectively weaken the randomness of the original data sequence, and the memory function in the self-memory algorithm breaks through the limitation that the traditional grey model is sensitive to the initial value. The results show that the number of elderly people in Nanjing's administrative districts will show a high base and high growth trend in the next 10 years. There are significant differences in the density of elderly people among the administrative districts. The density of elderly people in the central city is higher and becomes a dense area for the elderly, and the population density gradually decreases with the direction of suburban areas.

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4. Grey Clustering of the Variations in Reverse Pyramid Boarding Method Considering Pandemic Restrictions

Camelia Delcea, Liviu-Adrian Cotfas, Rafał Mierzwiak, Corina Ioanas

The Journal of Grey System 2022, 34 (1): 53-69.

摘要（179）

The COVID-19 pandemic has significantly hit the airline industry mostly due to the reduced number of flights between regions, the implementation of different protocols, restrictions, and the reluctance of the passengers to travel by airplane. In this context, the airlines have tried to offer an appropriate environment for their customers by ensuring a safe boarding process while considering the imposed restrictions related to social distancing. According to the literature, the Reverse Pyramid boarding method offers superior results in terms of boarding time and health risks in times of pandemics when compared to other classical airplane boarding methods. As the variations in Reverse Pyramid implementation are numerous, the present paper aims to determine which of these variations can be used when the airplane boarding process is made through the front door of the airplane. For this purpose, an agent-based model is created and used for simulating the variations in the Reverse Pyramid boarding method, while grey clustering is applied for dividing the variations into categories based on their performance. Three performance indicators, as reported in the scientific literature related to airplane boarding in times of COVID-19, are used, namely the boarding time, aisle seat risk, and window seat risk. Different scenarios are presented and analyzed in depth.

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5. Prediction of Mine Gas Concentration Based on Multi-variable Time-delayed DOGM(1, N) Model

Zhiming Wang, Yanzi Miao, Shoujun Li, Wei Dai, Shan Li, Yue Wang

The Journal of Grey System 2022, 34 (1): 70-83.

摘要（213）

Accurate underground gas concentration change prediction is essential for achieving safe and efficient production. Actual downhole systems often have time lags in the causal effects between variables, which may lead to poor performance of the traditional grey prediction model and affect the subsequent production and optimization operations. Under the time lag characteristics of the traditional grey prediction model, to solve the problems of the unclear mechanism of the driving term, as well as the deficiency of introduction rule. A new multivariate grey prediction DOGM(1,N) model with time lag characteristics is proposed in this paper. Based on the traditional OGM(1,N) model, the time-delay parameter is introduced into the driving term sequence. In order to solve the lack of analysis of the complete process of identifying the driving term sequence in the existing multi-variable grey model with time delay, this paper proposes a method for identifying the time-delay parameters and related factors sequence of driving term based on grey correlation analysis. Finally, the effectiveness of the method proposed in this paper has been verified by the simulation study of downhole gas concentration prediction. The results show that the DOGM(1,N) model has high prediction accuracy for the prediction problem of a small sample multivariable system with time-delay characteristics.

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6. A Conformable Fractional Grey Model CFGM(\alpha,\gamma) and Its Applications in Forecasting Regional Electricity Consumption of China

Wenqing Wu, Xin Ma, Bo Zeng, Hui Zhang, Gaoxun Zhang

The Journal of Grey System 2022, 34 (1): 84-104.

摘要（260）

This paper proposes a conformable fractional-order grey system model abbreviated as CFGM(\alpha,\gamma), which is an extension of the integer-order GM(1,1) model. The explicit expressions of the time response function and the restored values are derived by defining the conformable fractional-order derivative and accumulation. By using the least square estimation method, linear system parameters are derived, and then the ant lion optimizer algorithm is applied to search nonlinear system parameters. The effectiveness and feasibility of the CFGM(\alpha,\gamma) model are verified with seven-time series of the M3-Competition. Finally, the new model is applied to the electricity consumption of China. With data from 2009 to 2018, we establish 21 subcases for each selected province and calculate its overall performance, which shows that the new model is more stable than the GM(1,1) and FGM(q,1) models and can obtain competitive results.

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7. The Fractional Accumulative Time-Delay GM(1,N) Model and Its Application

Jiakang Song, Mingli Hu

The Journal of Grey System 2022, 34 (1): 105-113.

摘要（146）

Aiming at the problem of modeling small sample systems with time-delay cumulative effects, this paper introduces a time-delay coefficient control term and a fractional cumulative generation operator. The paper also proposes a fractional accumulative time-delay GM (1,N) grey prediction model, using particle swarm optimization algorithm to determine the optimal time-lag effect control coefficient 𝜆 and the optimal fractional order r. Finally, combining the GDP, Fixed Asset Investment and General Public Budget Expenditure of Jiangsu province from 2013 to 2020 to establish a forecast model, and comparing the prediction results of the GM (1,1) and GM(1,N) model shows that The Fractional Accumulative Time-delay GM(1,N) model (FATGM(1,N)) can better solve the small sample multivariate with cumulative timedelay characteristics system prediction problem.

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8. A Large-scale Group Grey-DEMATEL Decision Framework for Analyzing Factors Affecting Pandemic Control: A Case in Ghana during COVID-19

Jinmuzi Zhang, Bismark Appiah Addae, Ginger Y. Ke, Lingyao Liu, Haiyan Xu

The Journal of Grey System 2022, 34 (1): 114-138.

摘要（206）

Aiming at the pandemic control as a complex interactive relationship problem with high uncertainty and usually involving a large number of decision makers, this study integrates grey theory, large-scale group decision-making and DEMATEL method to innovatively propose a new large-scale group Grey-DEMATEL decision framework, which can examine the interdependence of relationships and system components. The framework mainly uses the grey relational clustering method to cluster large-scale group decision makers, so as to gather the decision makers’ evaluation information on factors and construct the relevant DEMATEL matrix to extract the key factors. In addition, under the proposed framework, a detailed inspection of the actual situation in Ghana was carried out. Through a comprehensive review of relevant literature and the actual situation in the country, a series of factors that affect the detection and control of COVID-19 have been identified and explained. Then use the proposed decision-making framework to extract the key factors, which are formally listed as priorities, so that policymakers can invest scarce resources. The results of detailed case studies and policy recommendations on the situation in Ghana prove the effectiveness of this novel approach.

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9. Commonality Refinement and Code Reuse of Grey Prediction Model Based on MATLAB

Shuangyi Yang, Bo Zeng, Shuliang Li, Sifeng Liu, Hanif Heidari

The Journal of Grey System 2022, 34 (1): 139-153.

摘要（300）

This paper realizes the rapid development of the MATLAB of grey prediction models through public module call. Firstly, the multiple modeling steps of grey prediction models are divided into three types: Model, View, and Controller. Then, it is analyzed which steps are completely common to all models. Finally, these steps are encapsulated into general modules similar to JavaBean. These modules can be called program building blocks for compiling grey prediction modeling software, which greatly improves the development efficiency, reduces code redundancy, and improves the stability of the software. This is of great value to the popularization of grey prediction models.

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10. Service Quality Evaluation of Medical Caring and Nursing Combined Institutions for the Aged Based on IVPFS-DEMATEL and Two-Stage Decision Model with Grey Synthetic Measures

Lan Xu, Long Yang

The Journal of Grey System 2022, 34 (1): 154-172.

摘要（240）

Aiming at the ambiguity, uncertainty, and grey characteristics in the service quality evaluation process of medical caring and nursing combined institutions for the aged, a service quality evaluation method is proposed through the interval-valued Pythagorean fuzzy set (IVPFS)-decision-making trial and evaluation laboratory (DEMATEL) and a two-stage decision model with grey synthetic measures. Based on the SPO model(structure-process-outcome), a service quality evaluation index system for medical caring and nursing combined institutions for the aged is established. Further, a new method is proposed to determine the index weight through combination of IVPFS and DEMATEL, followed by the two-stage decision model with grey synthetic measures is used to assess the service quality of medical caring and nursing combined institutions for the aged. Taking medical caring and nursing combined institutions for the aged in four typical cities of Jiangsu Province as target examples, the effectiveness of the proposed model is verified by comparing with other method. The results show that the proposed methodology can effectively evaluate the service quality of medical caring and nursing combined institutions for the aged.

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11. Carbon Emission Prediction Method of Regional Logistics Industry Based on Improved GM(1, N) Model

Xueqiang Guo, Bingjun Li

The Journal of Grey System 2022, 34 (2): 1-9.

摘要（517）

Aiming at the poor prediction performance of the traditional GM(1,N) model, this paper proposes the GM(1,N) model with expression optimization: firstly, unknown parameters are introduced into the coefficient matrix of the traditional GM(1,N) model to obtain the model expression with unknown parameters; Then the average relative error function with unknown parameters is constructed; Finally, the particle swarm optimization algorithm is used to obtain the parameter column with the smallest average relative error. Taking the carbon emission of the logistics industry in Hubei Province as an example, this paper forecasts the carbon emission by using the traditional GM(1,N) model, GM(1, N) model with background value optimization, and GM(1, N) model with expression optimization. By comparing and analyzing the prediction results of the three models, it is concluded that GM(1,N) model with expression optimization has better prediction performance.

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12. Criticality Analysis of Degrading Components in the Context of Uncertainty

Qi Li, Sifeng Liu, Yingsai Cao, Zhigeng Fang

The Journal of Grey System 2022, 34 (2): 10-21.

摘要（242）

A novel approach to measuring the criticality of degradation components is proposed in this paper to specify the contributions with regard to the decline of system reliability. Firstly, linguistic variables which are expressed by fuzzy set with grey number elements are introduced to assess the reliability of degrading components. Then the reliability of system is obtained based on structure functions. Thirdly, the cooperative game theory is employed to explore how a specific degrading component contributes to the degradation of system reliability in the context of uncertainty. The operations of fuzzy set and grey number are both used to obtain the component criticality. At last, an illustrative example about a newly-developed exoskeleton robot is presented to demonstrate that the proposed method is more rational and effective on measuring the criticality of components in the context of uncertainty.

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13.

Hyper-Spectral Estimation Model of Soil Organic Matter Based on Generalized Greyness of Grey Number

Wenjing Ren, Xican Li, Jieya Liu, Tianzi Ding

The Journal of Grey System 2022, 34 (2): 22-40.

摘要（192）

Due to the complexity of society and the high degree of uncertainty of the issues faced, precise numbers are, in many cases, difficult to describe their nature. And to deal with the problem that the existing interval grey number distance method does not reflect the characteristics of interval grey number well. This paper introduces a distance entropy to assign different weights to the upper and lower bounds and the kernel. To prevent the extreme value bias of the grey correlation coefficients, we propose a relative weight to constrain the extreme values. Considering the loss aversion of decision-makers, an extended TODIM is proposed, which combines the corresponding gains and losses to obtain the perceived dominance degree. From the method proposed in this paper, the perceived dominance degree is established to provide the ranking of the decision alternatives. A case of selecting an artillery weapon for a certain unit is used to validate the proposed method, followed by a comparative analysis.

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14. A Grey Correlation Method-Based Interval Grey Number TODIM Multi-attribute Decision Making Method

Qiuhong Zheng, Quanyu Ding, Yingming Wang

The Journal of Grey System 2022, 34 (2): 41-58.

摘要（253）

To overcome the uncertainty in the spectral estimation of soil organic matter, the hyper-spectral estimation model of soil organic matter content is established using grey system theory. Firstly, after introducing the generalized greyness of grey number, the properties of the generalized greyness are analyzed. Secondly, the modeled samples are ranked in the smallest to the largest in terms of soil organic matter content, the moving variance of the ranked estimators is calculated, the greyness of the lower, value and upper domains of the estimators is calculated based on the moving variance, and the new estimators are constructed based on the greyness. The estimation model of soil organic matter content is built and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient. Finally, the model is applied to estimate soil organic matter content in Zhangqiu District of Jinan, Shandong Province. The results show that the generalized greyness of grey number can effectively represent the interval grey number, reduce the random error and grey uncertainty of the estimation factor, and the accuracy of the proposed estimation model and test accuracy are significantly improved, where the determination coefficient R2 = 0.929 and the mean relative error MRE = 6.830% for the 12 test samples. The results further enrich the grey system theory, and provide a new way to modify the estimation factors and improve the spectral estimation accuracy of soil organic matter.

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15. Multi-attribute Decision Analysis on Three-Parameter Interval Grey Number Based on Bell-Shaped Possibility

Fenyi Dong, Linlin Wu, Huanhuan Liu, Han Shen, Zhenjie Zhai

The Journal of Grey System 2022, 34 (2): 59-74.

摘要（242）

Aiming at the multi-attribute decision-making problem of three-parameter interval grey number with completely unknown attribute weights and unknown attribute values of upper and lower limits and “center of gravity” points, a multiattribute grey target decision-making method with bell-shaped three-parameter interval grey number attribute values is proposed. Firstly, the three-parameter interval grey number with bell-shaped is constructed, and the possibility of the upper and lower limits and “center of gravity” points are discussed, and a new distance measure formula of the three-parameter interval grey number is defined. Secondly, according to the principle of maximum entropy, the objective programming model is constructed to determine the attribute weight. Then, the schemes are sorted according to the size of the comprehensive bull’s-eye distance. Finally, taking the rank of the possibility of ice jam disaster in the three reaches of the Yellow River as an example, shows that the model has more practical significance.

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16. A Grey Incidence Model for Panel Data Based on the Curvature of Discrete Surface

Honghua Wu , Zhongfeng Qu

The Journal of Grey System 2022, 34 (2): 75-87.

摘要（238）

To determine the relationship between panel data, a grey incidence analysis model based on the curvature of the discrete surface, namely the grey discrete curvature incidence model (GDCI), is proposed in this paper. Firstly, panel data are projected as discrete triangular surfaces. Secondly, based on the Mean curvature and the Gauss curvature of the discrete surface, the coefficient formulae of grey incidence of the Mean curvature and the Gauss curvature are respectively constructed. Then, two grey incidence models based on the Mean curvature and the Gauss curvature are established, respectively. Subsequently, a grey incidence model is proposed based on the curvature of discrete surfaces for panel data. The properties of the proposed model, e.g., normality, symmetry, similarity, and invariance to translation, are also discussed. Finally, both a numerical example and a practical example are given to illustrate the effectiveness and rationality of the proposed model. These examples also indicate that the proposed model can reflect the relationship between the panel data.

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17. A Novel Grey Multi-Dimensional Taylor Network Scheme for Nonlinear Time Series Prediction in Industrial Systems

Chenlong Li, Xiaoshuang Ma, Changshun Yuan, Bingqiang Wang, Chen Liu, Feng Wang, Wenliang Chen

The Journal of Grey System 2022, 34 (2): 88-107.

摘要（200）

A novel grey multi-dimensional Taylor network (MTN) scheme for nonlinear time series prediction in industrial systems is proposed in this paper. First, we construct the grey MTN model: 1) the GM(1,1) model is used to gain the prediction value and as a group of inputs for the MTN prediction model, which improves the prediction accuracy; 2) we take the MTN model as the prediction model and the conjugate gradient (CG) method as its learning algorithm. Second, the variational mode decomposition (VMD) method is used as data preprocessing for inputs of the prediction model, and the processed data are normalised. Finally, the actual prediction values are obtained by reverse normalization processing. Industrial examples are presented to verify the effectiveness of the proposed scheme. The experimental results show that the proposed prediction scheme is effective. Meanwhile, compared with other schemes, the proposed scheme improves the prediction accuracy and performance considerably.

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18. Innovation Ability of Strategic Emerging Industrial Cluster Based on 2-Mode Network and Three-Dimensional Grey Correlation Model

Si Jing, Lirong Jian

The Journal of Grey System 2022, 34 (2): 108-121.

摘要（228）

Due to the strategic emerging industrial cluster includes different types of subjects, their interaction will affect the industrial economy and innovation capacity. According to the data of strategic emerging enterprises, this paper constructs the economic 2-mode network and innovative 2-mode network composed of the strategic emerging industries and regions, respectively, according to the main business income and the number of effective patents of enterprises. Using the centrality of social network analysis to measure the structural characteristics of the 2-mode network, this paper analyzes the development status and evolution trend of strategic emerging industrial clusters. Then the three-dimensional grey correlation model is used to evaluate the innovation ability of each region with strategic emerging industrial clusters. Finally, an empirical study is carried out with Jiangsu province's strategic emerging industrial cluster as a typical case. The results show that: (1)The new generation of informational technology, biological industry, and high-end equipment manufacturing industry all have high centrality in the network, and they are located in an important position in the network. It shows that these three industries have strong economic effects and innovation ability and have a strong ability to control inter-enterprise and inter-regional informational transfer, while the digital creative industry has low centrality and is still in its initial stage located at the edge of the network. (2) The network centrality of Nanjing and Suzhou has always ranked first and second, indicating that these two regions have the highest influence on the network. The strategic emerging industrial clusters of Nanjing and Suzhou are relatively well-developed, and the innovation and economy have formed a positive interaction effect in these industrial clusters. (3) The innovation ability of strategic emerging industrial clusters in Suzhou, Wuxi, and Nanjing is relatively strong, while the innovation ability of strategic emerging industrial clusters in Taizhou and Yancheng is relatively weak. There is a great difference between southern Jiangsu and northern Jiangsu.

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19. Use Grey Incidence Analysis to Explore the Impact and Control of Hand, Foot, and Mouth Disease in Guangdong Province

Xiaowei Zhang, Xiaoyi He, Zidan Yang, Kaiting Zhang, Yandong Luo, Shangmin Chen, Liping Li

The Journal of Grey System 2022, 34 (2): 122-135.

摘要（266）

The hand, foot, and mouth disease (HFMD) epidemic has become a serious public health problem worldwide with a high economic and health burden. In addition, the prevalence of HFMD varies greatly between cities. Therefore, this paper aims to reveal high-risk cities for HFMD and associated meteorological and air pollution factors in Guangdong Province during 2014-2018. Data on the incidence of HFMD and meteorological and air pollution factors were obtained from the Guangdong Provincial Center for Disease Control and Prevention and Guangdong Meteorological Service. Three different grey incidence analysis (GIA) were used, namely Deng’s grey incidence analysis, absolute degree of GIA, and second synthetic degree of GIA. Additionally, GM(1,1) model was used to predict the trend of HFMD in 2019-2028. According to the second synthetic degree of GIA, the top three cities most affected by HFMD are Zhuhai, Guangzhou, and Foshan. However, the prediction model found that the incidence of HFMD in Guangdong Province will generally decline in the next 10 years, indicating that the prevention and control measures are still relatively in place. Deng’s grey incidence analysis found that CO, SO2, PM2.5, PM10, and wind scale are closely related to the incidence of HFMD. It is recommended to closely monitor weather change and urban air quality and take protective measures against HFMD in advance. The results of this study have substantial implications for the control of HFMD.

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20. An Improved Algorithm of Interval Grey Number

Li Li, Xican Li

The Journal of Grey System 2022, 34 (2): 136-152.

摘要（256）

Aiming at the limitations of the algorithm of interval grey number, an improved algorithm is introduced in this paper. Firstly, the limitations of the algorithm of interval grey number are analyzed, such as irreversibility, virtual amplification, and non-closure. Then, according to the "using minimum information principle" and the algorithm of a real number and its internal requirements, an improved algorithm of interval grey number is given, and some properties of the improved algorithm of interval grey number are discussed. Finally, some examples are given to verify the effectiveness of the new algorithm. The results show that the improved algorithm of interval grey number overcomes the limitations of the existing algorithm, and the calculation examples show that the improved algorithm is feasible and effective. The research results further enrich the grey system theory and provide a theoretical basis for studying grey algebra.

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21. A Clustering Evaluation Models for Grey Panel Data Based on the Possibility Function

Lirong Sun, Wencheng Li, Jiahui Ma, Danlei Feng

The Journal of Grey System 2022, 34 (3): 1-20.

摘要（226）

For data with the characteristics of "small sample, poor information," the concept of grey panel data is proposed, and a clustering method with the grey panel data based on the possibility function is developed. First, the application range of the possibility function is expanded, and a possibility function based on the interval grey number is derived. Afterward, aiming at the problem that the existing model cannot be applied to the grey panel data directly, a method for determining cluster weights of the grey panel data is proposed. According to the principle of new information priority, the grey cluster coefficient matrix at different moments is integrated to obtain the comprehensive grey cluster coefficient matrix. Finally, the objects are divided into grey categories under the grey cluster coefficient maximization principle. The proposed method is applied to the air quality assessment of eight major cities in China. Compared with the traditional panel data clustering method, it is found that the proposed method can refine and stratify the quality of the clustering results, which can make the clustering results clearer and easier to understand.

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22. Bayesian Network Model of China’s Financial Risk Under COVID-19 Based on Grey Clustering

Shuli Yan, Jiacheng Feng, Na Zhang, Xiangyan Zeng

The Journal of Grey System 2022, 34 (3): 21-35.

摘要（166）

The panic caused by COVID-19 and the stagnation of business activities induced the continuous breeding of China’s financial risks. This paper considers the COVID-19 and economic indexes as nodes to establish the Bayesian topology of financial risk. The liquidity, sovereign, and stock market risks are mainly considered to evaluate the financial risk. Based on the risk characteristics, the central interval trapezoidal possibility functions are designed, then the grey clustering model is used to classify the financial risk into four different levels. The possibility distribution of financial risk levels under different COVID-19 index levels is inferenced through the Bayesian network. Finally, each node’s monthly time series data from October 2019 to May 2021 is used to learn by NETICA software, and the conditional probability of each node and the possibility of financial risk are deduced. It is concluded that liquidity risk and sovereign risk are more sensitive to COVID-19, while the stock market risk is not very sensitive to it.

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23. Prediction and Analysis of Cerebrovascular Disease Mortality Based on Grey Model

Xuejun Shen, Honglin Hu, Chunyi Huang, Hongyue Yan, Shuyi Zhou, Jufang Li, Weiping Li, Xuerui Tan

The Journal of Grey System 2022, 34 (3): 35-46.

摘要（118）

This paper aims to explore the optimum modelling data for predicting cerebrovascular disease mortality in China by using GM(1,1) model. Also, it will discuss the applicability of grey relational analysis to analyze the related factors of cerebrovascular disease mortality. The subsequence sets with different data lengths were used to establish rolling GM(1,1), and predictive efficiency was judged by prediction error. Grey relational analysis was used to analyze the interrelationships between population, health expenses, environmental pollution factors and mortality. Results show that GM (1,1) grey prediction model can well predict the mortality of cerebrovascular diseases in China, especially when the modelling data is 8, the overall prediction effect is the best. In recent years, the prediction effect of 4 or 5 data modelling is better than that of more data modelling. Grey relational analysis suggests that population aging has a greater impact on the mortality of cerebrovascular diseases than other risk factors. The grey system theory is suitable for the epidemiological study of cerebrovascular diseases.

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24. BOPS Channel Strategies for Manufacturers and Online Retailers Under Omnichannel Operations Using Grey Game

Yinhai Shen, Qing Zhang

The Journal of Grey System 2022, 34 (3): 47-65.

摘要（144）

Both traditional manufacturers and online retailers have been implementing omnichannel strategies such as Buy-Online-and-Pick-up-in-Store (BOPS). By introducing interval grey numbers to represent consumer preference, which depicts uncertain consumer valuation, and the wholesale price and selling price constitute the profit function, we develop a basic dual-channel and three omnichannel grey models. Compared with the traditional online or offline dual-channel supply chain, the construction of the omnichannel model considers agency selling agreements and spillover effects as well. Four propositions have been proposed and proven through the analysis of the position degree analysis of the grey game model. Equilibrium analysis indicates that there is no option of [BOPS, No BOPS] in the equilibrium strategy of the grey game. Finally, a case study and numerical simulation are given to verify the model and reveal the relationship between the profit function and BOPS channel agency fees when reaching an equilibrium strategy.

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25. A Bibliometric Analysis on Grey System Theory and Its Application in 1982–2021

Yuying Yang, Naiming Xie, Bin Liu, Caorui Liu

The Journal of Grey System 2022, 34 (3): 66-80.

摘要（131）

This paper analyses the development level and trend of grey system theory (GST) over the past 40 years based on bibliometrics. Literature was searched using the Web of Science (WoS) databases. Literature analysis was carried out from eight aspects: paper publication, main journals publishing GST and its application, 20 highly cited articles, hot research topics, high-output scholars and their cooperation networks, the geographical distribution of scholars, funding agencies, and a comparison between papers obtained from the China National Knowledge Infrastructure (CNKI) and WoS databases. Bibliometric analysis showed that while GST had developed slowly over the initial 20 years, it experienced a period of high-speed development over the last 20 years. Two journals—the Journal of Grey System and Grey Systems: Theory and Application—play key roles in promoting the international development of GST. Professor Sifeng Liu and Nanjing University of Aeronautics and Astronautics have been the most influential scholar and research center in GST, respectively. GST has attracted many scholars worldwide, and the number of papers published in international journals is increasing. A comparison of publications related to GST between CNKI and WoS databases showed that more efforts are required for GST to become more international.

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26. A Watermarking Algorithm Using QR Code and Grey Relational Analysis in DCT Domain

Qiuping Wang, Fan Tang, Fang Dai, Xiaofeng Wang

The Journal of Grey System 2022, 34 (3): 81-94.

摘要（140）

An image watermarking algorithm in a discrete cosine transform domain based on QR code and grey relational analysis is presented in this paper. Literal information is encoded with a QR code as the digital watermark, and the watermark image is scrambled before embedding. The host image is divided into some non-overlapping blocks, and each block is processed with a two-dimensional discrete cosine transform. According to the correlation among image pixels, non-smooth regions of the host image are selected to embed watermark information by computing a double-direction grey correlation degree. Watermark embedding is selected from two schemes. One is based on the singular value decomposition (SVD), and the other is based on the orthogonal triangle decomposition (QR decomposition). Contrast experiment results show that the watermarking algorithm named QR code-GRA-SVD using the watermark embedding scheme based on singular value decomposition not only ensures the imperceptibility of the watermarking algorithm but also owns strong robustness.

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27. Construction and Application of a Time-Delayed Grey Bernoulli Model With Dummy Variables

Xue Bai, Shi Yao, Ye Li

The Journal of Grey System 2022, 34 (3): 95-114.

摘要（98）

To address the issue that the traditional grey model is difficult to predict nonlinear data series with multiple mutations caused by policy evolution, a time-delayed grey Bernoulli model with dummy variables (abbreviated as DTD-NGBM(1,1)) is proposed by introducing policy effects as dummy variables. Next, the solution of the time response function of DTD-NGBM(1,1) is discussed, and the optimal values of the time-delayed term and the nonlinear parameter are determined using the debugging method and the genetic algorithm, respectively. Finally, the validity and superiority of the proposed model are verified by taking solar power generation volume forecasting in China and the U.S. as examples. The results show that the proposed model can accurately describe the trend of the data series under the influence of dummy variables.

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28. A Review of Grey Target Decision Model

Sandang Guo, Qian Li, Yaqian Jing, Liuzhen Guan

The Journal of Grey System 2022, 34 (3): 115-134.

摘要（141）

An increasing amount of papers described different ways to obtain the ideal scheme by grey target decision model but seldomly set out the relative benefits of each approach so that the choice of the approach seems arbitrary. Therefore, this study discusses various grey target decision techniques and guides researchers in choosing suitable techniques for different decision models. This paper reviews the literature about grey target decisions published from 2010 to 2020, particularly methodological innovation. These techniques are categorized by the five aspects of developing a grey target decision model: (i) main types of data, (ii) manipulation of data, (iii) determination of criteria weights, (iv) calculation of bull’s-eye-distance, and (v) hybrid models. These techniques are discussed in terms of their underlying principles, complexity, strengths, and weakness. Summary tables and specification charts are given to guide the selection of suitable techniques.

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29. A Novel Grey Seasonal Prediction Model for Container Throughput Forecasting

Yichung Hu, Geng Wu, Shuju Tsao

The Journal of Grey System 2022, 34 (3): 135-147.

摘要（141）

Containerization is regarded as an important driver of globalization and international trade, and it also drives the development of global ports. Seasonal container throughput prediction is crucial for planning and operation by port authorities, and for the strategies formulated by logistics companies. To accurately predict the seasonal fluctuations in port container throughput, we propose a novel grey seasonal model called, FNDGSM(1,1). The proposed model involves time item, cycle Hausdorff fractional accumulating generation, and seasonal dummy variables. The particle swarm optimization algorithm is used to obtain the optimized parameters. Experimental results demonstrate that the proposed seasonal grey prediction model performs significantly better than other prediction models with quarterly container throughput data.

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30. Forecasting Housing Prices in China’s First-Tier Cities Using ARIMA and Grey BR-AGM(1, 1)

Zhongqin Wen, Yichung Hu, Shuhen Chiang

The Journal of Grey System 2022, 34 (3): 148-173.

摘要（190）

Housing prices in China have grown rapidly and dramatically over the past two decades; at the same time, the housing sector has contributed greatly to China’s economy. Thus, the importance of exploring China’s housing question cannot be overemphasized. To better understand the dynamics of housing prices in China, we try to forecast housing prices in China’s first-tier cities: Beijing, Shanghai, Guangzhou, and Shenzhen, by means of rolling ARIMA models and Grey BR-AGM (1,1) model in order to compare their forecasting performances. The empirical results demonstrate that Grey BR-AGM (1,1) model outperforms other models with a quicker reaction to external policy shocks.

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31. A Framework of Grey Prediction Models on China's Population Aging Under the Perspective of Regional Differences

Weiliang Zhang, Sifeng Liu, Junliang Du, Lianyi Liu, Xiaojun Guo, Zurun Xu

The Journal of Grey System 2022, 34 (4): 1-.

摘要（445）

Population aging is a major social problem that China is facing. Scientific prediction and correct analysis of population aging are important for resource allocation, policy formulation, and service provision. To this end, this paper proposes a population prediction framework based on grey models to predict and analyze regional differences in China's aging status. Firstly, we construct three indicators, i.e., total population, aged population, and proportion of the aged population, to reflect the aging status of a region. Secondly, we develop a grey model framework to predict and analyze aging differences in the eastern, central, and western regions of China. Finally, according to the prediction and analysis results of the three aging indicators, we suggest some corresponding countermeasures to address the challenges of China's future aging problem.

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32. A Vetoed Multi-objective Grey Target Decision Model with Application in Supplier Choice

Baoan Huang, Jianjun Miao, Qingsheng Li

The Journal of Grey System 2022, 34 (4): 15-.

摘要（256）

A vetoed multi-attribute grey target decision method is proposed and demonstrated with a practical case study. Firstly, a classical multi-objective grey target decision model is introduced, then a veto function is defined with a hesitant region, which can accommodate some vagueness in the decision maker’s specification of this level to reject a scheme. Secondly, a vetoed synthetic effect measure matrix is obtained based on the veto function and the uniform effect measure. Finally, the proposed model is applied to a supplier selection problem for official vehicles. The decision method proposed in this study, which is expressed by the vetoed synthetic effect measure, is reasonable and useful in decision-making practice.

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33. A Novel Option Pricing Approach Using the Black-Scholes Model and Grey Forecasting Method

Xuemei Li, Hang Wang, Yun Cao

The Journal of Grey System 2022, 34 (4): 28-.

摘要（221）

China’s options market has developed rapidly since 2015, and options have become an important financial derivative. Accurate pricing of options is an important prerequisite for options hedging, risk management, and other functions. There is much uncertain information interference in the traditional option pricing process, which will cause large errors between the pricing result and the actual market delivery price: because grey system theory has a natural advantage in dealing with uncertain information, based on the classic Black–Scholes (B-S) option pricing model and grey forecasting method, a comprehensive option pricing B-S- RGM model is developed, and Shanghai Stock Exchange 50ETF data in China are selected as a case for empirical analysis. The empirical results show that the proposed B-S-RGM model herein can mine the uncertain information in the process of option pricing. Compared with the classic B-S model, the B-S-RGM pricing model has more accurate pricing results. The average relative errors of the B-S models in Sample A and Sample B are 10.37% and 18.29%, respectively, while the average relative errors of the four B-S-RGM models are all stable and within 5%. In addition, the stability of the B-S-RGM model is discussed. The B-S option pricing model suffers from instability, with the pricing errors increasing in pricing intervals further from the expiration date while the B-S-RGM pricing model maintains a high degree of stability in pricing intervals both further and closer to maturity. The conclusions have important applications for option pricing, and can broaden the application scope of grey system theory.

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34. A Grey Relational Analysis Method for Structural Stability Sensitivity of Cable-Suspended Camera Robots Including Presence of Cable Mass

Peng Liu, Xuhui Zhang, Xinzhou Qiao, Yuanying Qiu

The Journal of Grey System 2022, 34 (4): 47-.

摘要（190）

A cable-suspended camera robot with a large workspace is employed to realize mobile photographs, while the large-span cables with unilateral driving properties introduce many new challenges that need to be addressed, whose structural stability is one of the most critical challenges. As a result, this paper first presents a stability measure method for camera robots while considering the cable mass and sags. Moreover, a stability sensitivity evaluation model for the robot is established with grey relational degree, where the relationship between the stability of the robot and the influencing factors (the cable tensions and the positions of the camera platform) is explored. Finally, the proposed models are supported by doing some simulation studies on a cable-suspended camera robot. The results show that the cable sags of the large-span cables have significant effects on both the cable tensions and the structural stability of the robot, while the stability sensitivity evaluation results indicate the cable tensions have a more important influence on the stability of the camera robot than the positions of the camera platform.

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35. Prediction and Analysis of Agricultural Eco-Efficiency in Henan Province Based on GM-BP Neural Network

Bingjun Li, Wenyan Li, Yifan Zhang

The Journal of Grey System 2022, 34 (4): 71-.

摘要（172）

The grey GM(1, 1) model is widely used due to its relatively simple structure, few parameters, easy training, and considering the grey characteristics of known information and unknown information. However, the GM(1, 1) model is weak in mining complex information, and it is difficult to deal with sequences with both linear and nonlinear characteristics. In response to this problem, the BP neural network is introduced, and the combination model of the GM-BP neural network is constructed by using the powerful nonlinear data mining ability of the BP neural network. And the GM-BP neural network is used to predict the agricultural eco-efficiency of Henan province. On this basis, the development trend of agricultural eco-efficiency in Henan is analyzed. The results show that the GM-BP neural network model can describe the complex changes in agricultural eco-efficiency in Henan and has a good prediction effect. The agricultural eco-efficiency in Henan from 2020 to 2025 is effective, with a continuous upward trend, but the increasing rate has slowed down. In space, the agricultural eco-efficiency of Henan shows the characteristics of gradually increasing from north to south, high in the east and west, low in the middle, and slightly higher in the west than in the east.

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36. A Self-Adaptive Grey DBSCAN Clustering Method

Shizhan Lu, Longsheng Cheng, Zudi Lu, Qifa Huang, Bilal Ahmed Khan

The Journal of Grey System 2022, 34 (4): 90-.

摘要（235）

Clustering analysis, as a classical issue in data mining, is widely applied in various research areas. This article proposes a self-adaptive grey DBSCAN (SAG-DBSCAN) clustering algorithm by introducing a grey relational matrix to obtain the grey local density indicator. We then apply this local indicator to have self-adaptive noise identification to gain a dense subset of the clustering data set. An advantage of this algorithm is that it can automatically estimate the parameters utilized to cluster the dense subset. Several frequently-used data sets are further examined to compare the performance and effectiveness of our proposed clustering algorithm with those of other state-of-the-art algorithms. The comparisons indicate that our new method outperforms other common methods.

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37. Dynamic Credit Evaluation Method for Small and Medium-sized Enterprises Based on Grey Cloud Similarity Analysis

Yeqing Guan, Yingjun Dai, Haotian Wu, Naiming Xie

The Journal of Grey System 2022, 34 (4): 103-.

摘要（116）

The solution of financing demand is one of the driving forces for the growth of small and medium-sized enterprises, and scientific and reasonable credit evaluation is an important way to alleviate the difficulty and expensive financing of enterprises. To address the uncertainty in enterprise credit evaluation, a dynamic evaluation method based on grey cloud similarity is proposed by combining grey incidence analysis and cloud model theory. Firstly, combining the expectation, entropy, and hyper entropy of the cloud model, the grey cloud similarity based on the inner or outer boundary curve is defined by drawing on the concept of the degree of grey incidence and the feature of the grey cloud similarity that can take the three digital characteristics of the cloud model into account, low computational complexity and high stability are summarized. Then, a multi-attribute comprehensive evaluation method is established considering randomness, fuzziness, and dynamic, and the dynamic evaluation information is aggregated by time-series weights to assess the rating of the evaluated object over a period of time. Finally, the feasibility and effectiveness of the proposed method are verified by the credit rating evaluation case of 10 small and medium-sized listed enterprises in the Growth Enterprise Market of Shenzhen Stock Exchange.

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38. n Incidence Degree With Fixed-ratio l-Order-Difference For Any l<=n and Its Properties

Yong Wei, Shasha Xi

The Journal of Grey System 2022, 34 (4): 118-.

摘要（121）

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39. The Application of Adaptive Generalized NGBM(1,1) To Sales Forecasting: A Case Study of an Underwear Shop

Ssu-Han Chen, Guo-Wei Chen, Yi-Ching Liaw, Jin-Kwan Lin, Shang-En Hsu

The Journal of Grey System 2022, 34 (4): 130-.

摘要（151）

This study develops a model to predict the weekly sales of an underwear shop in New Taipei City, Taiwan. Most commonly employed prediction methods failed when applied to the sales patterns of the case company and could not create an appropriate ordering strategy. This study is based on the assumption that the choice of a predictive model may need to be matched to the fluctuation structure of the data sequence. Not all data sequences are suitable for a single prediction model. An adaptive generalized Nonlinear Grey Bernoulli Model (NGBM(1,1)) is proposed for the case company. The training data sequences are fed into an Adaptive Resonance Theory 2 (ART2) model to generate typical templates. Simultaneously, the generalized NGBM(1,1) model is associated with the Real-valued Genetic Algorithm (RGA) to identify the best hyper-parameters for each training data sequence. The relationships between the typical templates and the 24 model types are mapped. In the testing stage, each data sequence is allocated to the most similar typical template using ART2 and mapped to the corresponding suitable model type, which makes a one-step-ahead prediction. The four-year weekly sales data of an underwear shop were empirically analyzed. The proposed method was compared with traditional prediction models. The experimental results show that the proposed method can provide more precise predictions.

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40. Security Risk Assessment for Trusted Chain Optimizing Based on Grey Fixed Weight Clustering

Guna Duan, Lizhong Duan, Wenan Zhou

The Journal of Grey System 2022, 34 (4): 147-.

摘要（128）

Trusted computing has received further attention as an effective technique to safeguard information systems, and it has been widely applied in various fields. Trusted chain establishment, as an essential model of trusted computing technology which ensures the credibility of computing platform, still brings poor system efficiency due to the complex environment of the platform. To optimize the procedure of trusted chain establishment for trusted computing platforms, our research improved traditional trusted chain establishment from static to dynamic with additional security risk level assessment step during trusted chain establishment innovatively. First, we comprehensively analyzed threats and their source for platforms. Based on main indicators of the platform, fixed weight clustering evaluation method in the grey system theory was used to evaluate security risk level for platforms. With the recorded data of software and hardware changes for the platform, we assessed the security risk level for this platform and demonstrated the clustering results and improved measurement strategy for platform during trusted chain establishment. It is more systematic and more efficient than the traditional static trusted chain establishment method, which could find more files tampered during measurement procedure.

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