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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.   Abstract （497）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （239）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （236）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （215）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （184）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （216）            Knowledge map    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. Related Articles | Metrics

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An Improved Algorithm of Interval Grey Number Li Li, Xican Li The Journal of Grey System    2022, 34 (2): 136-152.   Abstract （239）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （182）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （255）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （217）            Knowledge map    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. Related Articles | Metrics

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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 （414）            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 （123）            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 （147）            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 （242）            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 （204）            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 （138）            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 （115）            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 （214）            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 （109）            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 （179）            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