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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.   Abstract （137）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （101）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （177）            Knowledge map    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. Related Articles | Metrics

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

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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.   Abstract （163）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （241）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （159）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （219）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （196）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （143）            Knowledge map    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. Related Articles | Metrics

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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 （423）            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 （196）            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 （212）            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 （174）            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 （150）            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 （155）            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 （179）            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 （141）            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 （199）            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 （172）            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