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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-.   Abstract （359）            Knowledge map    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. Related Articles | Metrics

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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-.   Abstract （96）            Knowledge map    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. Related Articles | Metrics

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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-.   Abstract （105）            Knowledge map    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.  Related Articles | Metrics

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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-.   Abstract （173）            Knowledge map    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.  Related Articles | Metrics

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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-.   Abstract （165）            Knowledge map    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.  Related Articles | Metrics

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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-.   Abstract （105）            Knowledge map    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.  Related Articles | Metrics

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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-.   Abstract （85）            Knowledge map    Related Articles | Metrics

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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-.   Abstract （151）            Knowledge map    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.  Related Articles | Metrics

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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-.   Abstract （84）            Knowledge map    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.  Related Articles | Metrics

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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-.   Abstract （129）            Knowledge map    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.  Related Articles | Metrics

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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.   Abstract （62）            Knowledge map    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.   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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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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Study on the Strengthening Buffer Operators Based on Interpolation Functions Yanfang Wang , Xinyu Qi, Tao Chen, Hui Zhang, Zhengpeng Wu The Journal of Grey System    2023, 35 (2): 167-178.   Abstract （33）            Knowledge map    Based on the present theories of buffer operators, two kinds of strengthening buffer operators (SBOs) based on interpolation functions are established in this paper. Compared with the ones proposed by Dang, it shows that Dang's SBOs are, in our special case. The properties and the inner connections of different SBOs are discussed, which greatly extend the application range of the SBOs. The main function of the SBOs is to reduce or eliminate the impact of shock disturbed system, to restore the distorted "actual data" to its true state. This is the first time to connect the construction of strengthening buffer operators with interpolation functions, which provides a new routine for constructing SBOs.  Related Articles | Metrics

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Research on Grey Clustering Model Based on NDEA for Equipment System-of-Systems Configuration Selection Decision Jingru Zhang, Zhigeng Fang, Shuyu Xiao, Luyue Zhang The Journal of Grey System    2023, 35 (4): 91-107.   Abstract （54）            Knowledge map    Resources (e.g., development budget, equipment performance) is not infinite for the plan and development of equipment system-of-systems (ESoS). Decision makers (DMs) must determine the priority of the ESoS configuration scheme under many constraints. Aiming for this problem, a structure and operation logic modeling of ESoS is analyzed. The network DEA approach describes each ESoS as a n-phase network decision unit with inputs and outputs. Secondly, the performance and cost of single equipment and ESoS combat effect are all considered. Based on this, we calculate the input-output efficiency of ESoS and consider two situations regarding the development budget. Then, with phased efficiency as evaluation indexes, the grey clustering evaluation based on the possibility function is applied to measure the ESoS configuration from the perspective of DMs. Finally, a case study verifies the feasibility and efficacy of the proposed methodology via selection decision results. The proposed method can aid DMs throughout the decision process for ESoS.  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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AGMC Model for Forecasting Carbon Dioxide Emission in Northwestern China Kedong Yin, Haolei Gu The Journal of Grey System    2023, 35 (2): 1-13.   Abstract （32）            Knowledge map    With economic and social development rapidly, carbon dioxide emission soared in the northwestern region. The importance of adopting emission reduction strategies cannot be overemphasized. Therefore, it is essential to accurately forecast carbon dioxide emission in northwestern China. The study used Lasso parameter estimation to select influential carbon dioxide emission features. FGM(1,1) model was used to forecast features trend. The adjacent accumulation grey multivariate convolution model (AGMC) model forecasts carbon dioxide emission trend. The future two years forecast result shows that Shaanxi province’s carbon dioxide emission will show a fluctuating trend. Qinghai autonomous regions will show a decreasing trend. Other regions will be in upward trend. The study suggests the central government should pay attention to the carbon emission problem in the northwestern region. Government increases science and technology investment and pays attention to urbanization spatial pattern rational layout.  Related Articles | Metrics

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The Impact of Claim Management on Selecting Contractors Using the Grey Ordinal Priority Approach (OPA-G) Hamid Asnaashari, Abbas Sheikh Aboumasoudi, Mohammad Reza Mozaffari, Mohammad Reza Feylizadeh The Journal of Grey System    2023, 35 (2): 14-40.   Abstract （21）            Knowledge map    This study aimed to explore the causes and origins of claims in the oil and gas industry. It also sought to find solutions, reduce or eliminate claims, and use them to select efficient contractors. In this paper, one of the new multi-attribute decision-making methods, called the grey ordinal priority approach, was used to rank criteria and alternatives. For dealing with uncertainty, grey systems theory was also applied. Finally, some criteria were proposed to identify and select more efficient contractors. The Grey systems theory can reduce the incidence of claims and increase productivity by ranking claim solutions to reduce costs and execution time, increase quality, and use these solutions in selecting contractors. The variations between the “grey ranks” and the “targeted changes observed” showed that an increase in distance between the ranks increases the effect of the top ranks. Besides, the increase of the grey range of the total weights from [0.8, 1.2] to [0.5, 1.5] made the scores fluctuations regular, and the rankings were shifted to weaker ranks with the closest competition. The contributions of this study are as follows: (1) Unlike previous research that focused on prioritizing the causes of claims, this study tried to identify and rank solutions to reduce the occurrence of claims; (2) The recognized solutions were presented as criteria for selecting more efficient contractors; (3) grey ordinal priority approach method has been used to compare and rank the proposed solutions to increase productivity, considering cost, time, and quality criteria; and (4) This method was first used in project claim management. This method showed that the criterion of “Employing a technical team with experienced and educated members” has the first, and the criterion of “Ensuring the contractor’s effective service records” has the second rank. Related Articles | Metrics

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A Novel Grey Incidence Analysis Model Based on Gamma Probability Density Function and Its Application Yu Feng, Yaoguo Dang, Deling Yang, Junjie Wang, Huimin Zhou The Journal of Grey System    2023, 35 (2): 41-54.   Abstract （32）            Knowledge map    Aiming at the problem that existing grey incidence analysis methods cannot effectively characterize the difference of development trends between sequences in line with the normativity axiom, a novel grey incidence analysis model based on the Gamma probability density function (GIAMG) is proposed. First, the projection factor is defined based on the geometric projection between sequences. Then, the grey incidence coefficient (GIC) is designed by combining the projection factor and the Gamma probability density function. According to the difference in development trends in different periods, the degree of grey incidence is constructed by summing up the GICs with variable weight. Finally, the GIAMG is used to identify the main air pollutants for respiratory diseases in Tianjin, China. Experimental results show that the proposed model is superior in the reliability and effectiveness of the related order over four traditional incidence models.  Related Articles | Metrics

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Forecasting Productive Inventory by Using Graphical Evaluation and Review Technique with Grey Number Representation Jing Zeng The Journal of Grey System    2023, 35 (2): 55-67.   Abstract （26）            Knowledge map    Quantitative forecasting of the inventory for key products can help to reduce the amount of inventory obsolescence and prevent production delays due to raw material stock-outs. Predicting productive inventory is beneficial to promote the sustainability of production management. In this work, a prediction model is constructed that predicts the pass rate of products and the processing path of unqualified products and simultaneously calculates the quantity, time, and probability of each path. Using the Graphical Evaluation and Review Technique (GERT), the manufacturing process of a square tube can be transformed into a stochastic network. Then, grey parameters are introduced into the GERT network to solve uncertainty in manufacturing. Finally, a numerical example is given to obtain a productive inventory prediction for beam square tubes using grey GERT(G-GERT). The main contribution of this work is the integration of inventory quantity, time, and probability. These three results can be predicted simultaneously, and the algorithm can be extended to any product production network. Related Articles | Metrics