The Journal of Grey System

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1. 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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2. 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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3. 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（171）

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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4. 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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5. 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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6. 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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7. 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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8. 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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9. 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（115）

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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10. 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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11. Parameter Estimation of Integro-differential Equation-based Grey Predator-prey Model From Noisy Data

Zhaoya Zhang, Naiming Xie, Lu Yang, Xiaolei Wang

The Journal of Grey System 2024, 36 (2): 79-89.

摘要（99）

The grey predator-prey model is widely applied in many fields for its effectiveness. While most of the research on the grey predator-prey model focuses on the different model forms, less attention has been paid to identifying parameters and initial value from noisy data. In this work, considering the measurement noise in practice, we propose a two-stage approach to estimate the structural parameters and initial value of the grey predator-prey model with integro-differential equations(IDEs). First, by introducing an integral operator, we propose another form of the grey predator-prey model, namely the IDE-based grey predator-prey model. Next, we develop a parameter estimation approach based on the idea of a two-stage in the presence of measurement noise, where in the first stage we smooth time series using cubic B-Spline and in the second stage estimate structural parameters and initial conditions by the separable nonlinear least squares. Then, the finite sample performance of the IDE-based model is investigated with Monte Carlo numerical experiments. Results demonstrate that the IDE-based model has better performance in terms of accuracy than the Cusum-based model. Finally, we use a case to further verify the accuracy and stability of the proposed method.

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12. 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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13. 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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14. 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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15. 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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16. 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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17. 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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18. 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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19. 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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20. 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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