The Journal of Grey System

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1. An Improved Grey Time-Delay Multivariable Model and Its Application

Huimin Zhou, Haifeng Lin, Junjie Wang, Yaoguo Dang, Yingjie Yang, Yu Feng

The Journal of Grey System 2023, 35 (1): 1-19.

摘要（78）

An accurate output value prediction is of great significance for policy-making and plan development in high-tech industries. An adaptive cumulative time-delay discrete grey multivariable model is proposed to forecast the output value of hightech industries in China. Specifically, a new time-delay function is constructed to unify the time-delay effects and facilitate a realistic adaptation to disparate timedelay effects. Subsequently, the Grey Wolf Optimizer algorithm is used to find the optimal parameters for the new time-delay function, which improves the model’s adaptability. Furthermore, to further enhance the model’s prediction accuracy, an iterative reweighted least squares method is also adopted to optimize the parameter vector. To demonstrate the applicability of the proposed model, it is employed in hightech industries in China. The empirical findings show that the proposed model outperforms the benchmark models.

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2. Forecasting Seasonal Changes in Ocean Acidification Using a Novel Grey Seasonal Model with Grey Wolf Optimization

Kedong Yin, Kai Zhang, Wendong Yang

The Journal of Grey System 2023, 35 (1): 20-38.

摘要（121）

Ocean acidification forecasting has important implications for studying global carbon dioxide emissions reductions. However, due to seasonal and cyclical features, ocean acidification forecasting remains an extremely challenging task. Therefore, this paper proposes a grey wolf optimized fractional-order-accumulation discrete grey seasonal model (GFSM(1,1)). The GFSM(1,1) model improves the prediction of ocean acidification in two ways: The new information priority of seasonal data is improved by the fractional accumulation operator, and the adaptability of the grey model to seasonal data is increased by seasonal item parameters. The above two works have significantly improved the prediction accuracy of the grey prediction model for ocean acidification. The prediction results in practical cases prove that the prediction effect of the GFSM(1,1) model is not only better than the existing grey models (FMGM(1,N)、NSGM(1,N), and GM(1,1)) but also better than statistical models (Nonlinear regression and ARIMA), traditional neural network model (LSTM) and deep learning model (SVM). Finally, the GFSM(1,1) model is applied to the prediction of seawater acidification. The forecast results show that the ocean will be acidified at a rate of 0.001863 per year, and the pH of the ocean will decrease by about 0.03% per year compared to the same period in previous years.

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3. A Novel Negative Grey Relation Model for Reverse Sequences

Ningning Lu, Sifeng Liu, Junliang Du, Ding Chen, Xiaochao Qian

The Journal of Grey System 2023, 35 (1): 39-48.

摘要（81）

Grey relation analysis model is used to analyze the degree to which a factor affects the system. Negative grey relation model measures the relationship between reverse sequences. Considering the proximity of local changes and the trend of sequence development, the paper defines the relative change within the time domain and oscillation change between time intervals. So, a novel negative grey relation model is proposed both vertically and horizontally. In the end, we use the existing instance to verify the effectiveness of the model.

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4. Research on PEST·CRITIC-EGM(1,1) Method for Security Risk Warning of Regional Digital Economy

Fang Wang, Chengxuan Wu, Lili Liu, Jin Zhao, Yi Zhang

The Journal of Grey System 2023, 35 (1): 49-66.

摘要（150）

The regional digital economy security risk warning system has been established to strengthen the construction of safety shields for the regional digital economy and promote the sound and steady development of the digital economy. Based on the PEST analysis method, a regional digital economy security risk evaluation index system including four first-level indicators, 13 second-level indicators, and 49 third-level indicators are constructed. The index weight is determined by CRITIC method, the regional digital economy security risk index (DESRI) is established by integrated operation, and the prediction and early warning are realized by EGM(1,1) model. Through the data collection and empirical analysis of Shaanxi Province, it is found that: (1) The DESRI of Shaanxi Province showed an overall rising trend from 2017 to 2020, but the risk level was reduced from dangerous to a general level; (2) In 2021 and 2022, the security risk of the digital economy in Shaanxi Province is generally at the security level, among which the policy risk index and social risk index were at the security level, the economic risk index was in the serious level and the crisis level respectively, and the technical risk index was in the crisis level. The results of the empirical analysis verify the feasibility and effectiveness of PEST·CRITIC-EGM(1,1) Method, which can be used for the assessment and early warning of regional digital economy risks.

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5. Asymmetric Grey Evolutionary Game Models with The Limited Cognition

Qin Zhang, Zixin Bao, Zhigeng Fang, Sifeng Liu

The Journal of Grey System 2023, 35 (1): 67-81.

摘要（64）

With limited cognition, the group of players can only estimate the range of their payoffs instead of the specific values. Then we propose the asymmetric grey evolutionary game. Via the analysis of the equilibrium of this game, the single grey belt and crossed grey belt are found. Meanwhile, besides Nash equilibrium, we find a new equilibrium. When the group of players are in the crossed grey belt, they can’t obtain more profits no matter how they change the original strategies. Because their grey expected profits are always equal to the grey average expected profits. This is a short-term equilibrium due to limited cognition. Finally, we illustrate the asymmetric grey evolutionary game to analyze the effect of psychological contract breaches on employee turnover intention.

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6. An Optimized Non-Equidistant Grey Model of Population Aging in Inner Mongolia Based on All Previous National Censuses

Jun Zhang, Chaofeng Shen

The Journal of Grey System 2023, 35 (1): 82-100.

摘要（75）

The issue of population aging is related to the sustainable development of the future economy and society. It is necessary to conduct an in-depth analysis and prediction of the development trend of population aging. In this study, according to the small samples and non-equidistant characteristics of the data from the first to the seventh national censuses in Inner Mongolia, the fractional order non-equidistant GM(1,1) model with optimized background value (abbreviated as OBFNEGM(1,1) model) for the total population and the aging population in Inner Mongolia are established, and the system parameters of the OBFNEGM(1,1) model are calculated by using the whale optimization algorithm. The fitting results show that the mean absolution percentage error of the proposed model is lower than that of the classical non-equidistant GM(1,1) model. On this basis, in the future eighth national census, the total population, the aging population, and the proportion of the aging population in the total population are predicted, and the suggestions to deal with the aging of the population are put forward so as to adjust the corresponding policies and measures timely.

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7. An Extrapolation Non-Equigap Grey Model for Operation Management

Che-Jung Chang, Wen-Li Dai, Der-Chiang Li, Chien-Chih Chen, Guiping Li

The Journal of Grey System 2023, 35 (1): 101-112.

摘要（92）

Accurate short-term demand forecasting is crucial for the production plan development, but a shorter forecasting period implies that the product demands are more unstable and, thus, that ascertaining their developing trends is difficult. Therefore, using large historical observations to build forecasting models may not result in favorable forecasting performance. Prediction methods based on the latest limited data have thus become vital for maintaining management efficiency and competitive advantage. Grey system theory is a technique for resolving this difficulty. However, the conventional grey model is designed for time-series data featuring equigaps, which limits its application scope. Although in the current published research, scholars have proposed some non-equigap grey models; however, the newest datum is usually weakened to alleviate the randomness of data in these models, which may result in a larger prediction error. To conquer these shortcomings, this study introduces linear extrapolation to modeling procedures for emphasizing the importance of the newest datum and then proposes an improved non-equigap grey model. In the experiments of two real cases, the proposed method exhibits favorable forecasting performance, indicating a feasible solution for small non-equigap data forecasting.

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8. The Annual Sales Forecast for a Chinese Auto Parts Manufacturer Based on IGM (1,1)

Hongying Shan, Mengyao Qin, Libin Zhang Zunyan Meng, Peiyang Peng

The Journal of Grey System 2023, 35 (1): 113-129.

摘要（81）

Sales forecasts for auto parts manufacturers are critical to the overall health and sustainability of the auto industry. As a result, it has become critical to design a convenient and accurate forecasting model based on little historical data. By examining a modest amount of valid data, gray prediction theory can investigate the law of change. The Improved Grey Model (1,1) (IGM (1,1)) model is introduced in this study, which conducts a functional transformation on the original data series in order to create a new one with a high degree of smoothness. A genetic algorithm is utilized to establish the optimal parameter values for the background values, which enhances prediction accuracy. The model's predictive accuracy was evaluated using the annual sales of Company B, a Changchun-based auto parts manufacturer, from 2009 through 2020. The numerical findings indicate that the proposed method outperforms the four models regarding forecasting performance. Additionally, the proposed method is critical for conducting in-depth research, promoting, and implementing the gray model in auto parts manufacturing firms.

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9. A Laspeyres Index Decomposition-based Multivariable Grey Prediction Model for Forecasting Energy Consumption: A Case Study of Ghana

Jeffrey Ofosu-Adarkwa, Naiming Xie

The Journal of Grey System 2023, 35 (1): 130-155.

摘要（83）

Energy consumption is closely linked to a country’s economic activity. For most developing countries making efforts to shift to industry-driven economies, the relationship between energy consumption and economic activity cannot be overemphasized. This study, therefore, employs the Laspeyres Index Decomposition (LID) analysis to decompose the change in energy demand into five driving factors according to three effects. The derived factors are then combined with the first order multivariable grey forecast model to form the hybrid model, LID-GM(1,6). The model is applied to the energy consumption situation of Ghana as a case study. The decomposition analysis gives insight into which economic sectors are accountable for the energy demand changes that occurred during the period 2006–2019, and thus serves as a guide for policymaking. The significance of this paper lies in its contribution to the development of the GM(1,N) prediction models. The grey forecast model, based on factors derived from an index decomposition analysis, is used to predict total energy consumed annually in Ghana from 2020 to 2030. The LID-GM(1,6) is evaluated for forecast accuracy and compared with other models. The LID-GM(1,6) has an out-of-sample MAPE of 3.77%, signifying an accuracy of approximately 96%.

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10. An Improved Grey Incidence Clustering Approach for Technological Innovation Capability Assessment of China's Regional High-Tech Industry

Xu Dong-Liang

The Journal of Grey System 2023, 35 (1): 156-172.

摘要（86）

The development level of the high-tech industry affects the comprehensive competitiveness of a country and a region. It has great theoretical and practical significance to grasp the status quo and differences in technological innovation capability of regional high-tech industries in R&D and transformation and to provide a basis for relevant departments to formulate differentiated policies for developing high-tech industries. In order to comprehensively reflect the innovation capability and fully excavate and extract the differentiated information of China's regional high-tech industry. According to the characteristics and laws of panel data on the high-tech industry, from the two dimensions of technology R&D and achievement transformation, the grey incidence analysis method is exploited to a novel grey matrix type incidence clustering model based on the panel data for hightech innovation capability assessment and differences extraction. The result shows that the high-tech innovation capability is not strong on the whole, and there are obvious regional differences and imbalances in R&D and transformation, the ranking is in the order of eastern, central, and northwestern provinces and cities.

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11. AGMC Model for Forecasting Carbon Dioxide Emission in Northwestern China

Kedong Yin, Haolei Gu

The Journal of Grey System 2023, 35 (2): 1-13.

摘要（99）

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.

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12. 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.

摘要（58）

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.

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13. 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.

摘要（107）

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.

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14. 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.

摘要（65）

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.

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15. Identifying Influential Nodes in Complex Networks Based on Multi-Information Fused Degree of Grey Incidence

Jinhua Zhang, Qishan Zhang, Ling Wu, Lijuan Weng, Xiaojian Yuan, Jinxin Zhang

The Journal of Grey System 2023, 35 (2): 68-86.

摘要（77）

This paper proposes a new synthetic measure of node centrality, namely, multi-information fused degree of grey incidence centrality (MIFDC), which is used to evaluate the importance of nodes and identify influential nodes in complex networks. It is the first time that the grey incidence analysis (GIA) and the D-S evidence theory are combined to identify influential nodes in complex networks in the MIFDC method. The proposed MIFDC measure comprehensively considers the information of multiple centrality measures and can correct the subjective bias problem in the selection process of the grey incidence operator. To verify the performance of the proposed method, the MIFDC method is applied to identify influential nodes in two real networks, the Advanced Research Project Agency (ARPA) network, and the terrorist relationship network. The application results show that the MIFDC method can effectively identify the influential nodes of the network.

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16. Forecasting the Evolution of Public Opinion Using a Novel Improved Grey Model During Emergencies

Hongchan Li, Yu Ma, Haodong Zhu

The Journal of Grey System 2023, 35 (2): 87-104.

摘要（83）

Public opinion is an aggregate of people’s views, attitudes, and emotions about events that can spread through the Internet to generate online public opinion. Studying the evolution of online public opinion during emergencies can help relevant departments to take targeted measures to respond in advance. Tweets and Weibo texts with negative emotions are essential factors affecting the evolution of online public opinion. To this end, this paper proposes a novel improved grey model, SISGM(1,1), that optimizes initial conditions and background values for predicting the number of negative Weibo texts generated during emergencies. The model is improved as follows: First, the background value is reconstructed by the Simpson rule to achieve the effect of smoothing the data sequence. Second, the ISRU activation function is used to modify the initial condition, which can better reveal the characteristics of data growth and improve the model’s adaptability. Then, the modified background value is combined with the optimized initial condition to realize the double optimization. Finally, the PSO algorithm is used to calculate the introduced parameters to improve the prediction accuracy further. Additionally, the model is compared with five competing models to predict the evolution of online public opinion during emergencies. The experimental results demonstrate that the proposed model has apparent advantages compared to the other five competing models.

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17. A Grey Three-Way Decision Approach and Its Application

Xuege Guo, Yong Liu, Huanhuan Zhao, Hanru Zhang, Gang Zhao, Zhiying Han

The Journal of Grey System 2023, 35 (2): 105-129.

摘要（105）

The three-way decision offers new perspectives for solving uncertain decision problems, especially categorical decision-making. However, in reality, the preference information of the decision object may be vague and uncertain. To address this issue, we construct a grey relation analysis based three-way decision model in a grey system environment. First, based on an improved grey correlation similarity measure, we investigate how the conditional probabilities of decision events are constructed. Subsequently, according to the information entropy, we established the objective optimization model and calculated the optimal weight of each index. Considering the delay cost and the uncertainty of the loss function, the grey relative loss function matrix is constructed based on the uncertain information of decision objects. Based on this, we establish the optimal thresholds method with the relative loss function and devise the decision rules. Using the established decision rules, we can obtain the classification results of all decision objects. Finally, the proposed model is used to deal with the users’ classification problems in the movie recommendation system, which demonstrates the validity and feasibility of the model.

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18. Grey Clustering Analysis of Provincial Scientific and Technological Innovation Capability Mainland

Yuying Yang, Yuxuan Huang, Yichen Liu, Bin Liu

The Journal of Grey System 2023, 35 (2): 130-148.

摘要（126）

The scientific and technological innovation capabilities of different provinces and cities in China are quite different. Comprehensive evaluation and analysis of provincial scientific and technological innovation capabilities are conducive to a more comprehensive and targeted understanding of different regional differences and put forward more effective policy recommendations for balanced and coordinated regional development. Firstly, this paper constructs the evaluation index system of scientific and technological innovation ability from four aspects: innovation input, innovation output, innovation carrier, and innovation environment; Secondly, using the method of combining subjectivity and objectivity, the indicators are weighted to reflect the importance of different indicators on scientific and technological innovation capability; Finally, the paper uses the grey weight clustering method to analyze the scientific and technological innovation capacity of 31 provinces and cities mainland from 2010 to 2020. The study found that there are significant geographical differences in China's scientific and technological innovation capabilities. The provinces and cities with strong scientific and technological innovation capabilities are mainly Beijing, Shanghai, Jiangsu, Zhejiang, and Guangzhou, which can enhance the scientific and technological innovation capabilities of surrounding provinces and cities through regional synergy.

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19. Forecasting China’s Hydroelectric Power Generation Under the New Era Based on Grey Combination Model

Shuliang Li, Nannan Song, Ke Gong, Bo Zeng, Yingjie Yang

The Journal of Grey System 2023, 35 (2): 149-166.

摘要（184）

It's necessary to forecast hydroelectric power generation under the background of carbon peak. Firstly, based on the three-parameter whitening grey prediction model, the order of the accumulating-fractional-order in the real field and the coefficients of the background value are combined and optimized to establish a two-parameter optimized three-parameter whitening grey prediction model. The model is applied to predict China's hydroelectric power generation, and the comprehensive error is only 1.13%, indicating that the model has good performance. The results show that the carbon peak target can be achieved by 2030. Based on this, relevant countermeasures and suggestions are put forward.

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20. 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.

摘要（68）

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.

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21. Identification Research of China's Potential Autonomous and Controllable Key Products

Wenping Wang, Laifeng Wu

The Journal of Grey System 2023, 35 (3): 1-17.

摘要（142）

To comprehensively prevent and resolve the potential risk of a "bottleneck" in the context of reverse globalization, sorting out China's potential autonomous and controllable key products systematically is an important issue. The paper constructs a product space network model according to the data of 243 countries' export products from 1995 to 2019 and measures the product coreness based on the revealed comparative advantage of products to identify global core products. On this basis, the close degree of grey incidence model is used to quantitatively analyze the close correlation degree of the overall revealed comparative advantage distribution of countries in the global product system. And through the analysis of the marginal contribution of revealed comparative advantage, the study also identifies China's potential autonomous and controllable key products. Among the 124 global core products in the top 10% of the coreness in 2019, the products whose revealed comparative advantage changes make a greater contribution to the distribution of China's overall revealed comparative advantage are potential autonomous and controllable key products in China. Among the top 31 kinds of core products with the top 25% contribution rate, China's potential autonomous and controllable key products are mainly distributed in the fields of mechanical and electrical equipment, vehicles, aircraft and ships, optical and medical precision instruments with high-tech characteristics, as well as in the field of chemical products with capital-intensive characteristics.

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22. A Multi-Model Grey Fusion Forecasting Procedure for China’s Ecommerce Service Industry

Jianhong Guo, Tianci Li, Yingyi Huang, Chejung Chang

The Journal of Grey System 2023, 35 (3): 18-26.

摘要（115）

During the Covid-19 pandemic, the e-commerce service industry has played a significant role in ensuring the development of e-commerce and promoting the innovation of new business models. Grasping the trend of the future development of the e-commerce service industry leads to pushing the government to formulate industrial development strategies and to ensure the rapid recovery of the postepidemic economy. This paper proposes a Multi-Model Grey Fusion (MGF) procedure to solve the reliability and robustness problems of predicting the future trend of the e-commerce service industry. The experimental results show that MGF performs well in handling the small data prediction problem and that it is more reliable and robust than the four single-base models, which are the grey model, linear regression, back-propagation neural network, and support vector regression. The forecast by combining the MGF with the rolling framework shows that China’s e-commerce service industry will keep an excellent development momentum. Moreover, the market size is expected to reach RMB 8.78 trillion by 2025, with an average annual growth rate of 8.8%.

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23. Research on Grey Power Model Based on Periodic Wave Sequence and Its Application

Jiefang Liu, Rongrong Yang, Pumei Gao, Kun Yang

The Journal of Grey System 2023, 35 (3): 27-38.

摘要（106）

A new grey power model is proposed for modeling periodic small sample systems. In the modeling process, a trigonometric function is introduced to identify the periodicity characteristics of the data, and the specific time response formula and modeling steps are given. At the same time, in order to minimize the average relative error, the least square method and genetic algorithm are used to optimize and solve each parameter. Finally, the model is applied to forecast the traffic flow of the Hengda Expressway in Hebei Province and the PM2.5 content of air pollutants in Tianjin. The results are compared with those of other models. The results show that the proposed model has higher prediction accuracy, which further verifies the validity of the model.

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24. Forecasting Method Based on Attenuated LSTM for Time Series With Missing Data of Soil Organic Matter Based on Hyperspectral Data

Xin Liu, Yichao Ma, Jian Yu

The Journal of Grey System 2023, 35 (3): 39-53.

摘要（135）

Missing data presents a significant challenge when forecasting unknown data in time series. To address this issue, this paper proposes an Attenuated Long and Short-Term Memory model based on a decaying function, which is abbreviated as AD-LSTM, for forecasting unknown data in time series. As strong correlations exist in adjacent data, the Grey model is leveraged to predict and impute missing values in small-sample datasets. To improve the accuracy of forecasting in time series with missing data, we introduce subspace decomposition, which can correct errors in the memory state cell caused by missing elements, and a time decay function, which utilizes the number of adjacent continuous missing data as a weight to modify the memory cell and enables the model to detect the existence of missing elements, into the LSTM unit. These enhancements reduce the impact of imputed data on model training in time series analysis. Finally, to verify the effectiveness of our proposed method, we conduct experimental validation and comparative analysis using the Beijing house price dataset. Our results indicate that the AD-LSTM model performs better in reducing the impact of missing data and achieving lower forecast errors compared to the baseline models.

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25. A Grey Clustering Comprehensive Evaluation Methodology for Green Construction Based on Information Theory

Chenchen Jia, Jinfa Yao, Yongheng Wei, Bo Xie, Hazrat Bilal

The Journal of Grey System 2023, 35 (3): 54-70.

摘要（173）

With augmenting cognizance of environmental issues, there is a growing concern for sustainable construction due to the negative environmental impacts resulting from construction activities. Although green construction has been advocated globally, the lack of scientific and systematic green construction assessment tools is a key factor affecting the adoption of green construction. In this study, a methodology for green construction assessment was developed based on the grey system theory, which allows for a quantitative evaluation of environmental performance for construction activities. We integrate the advantages of both subjective and objective weighting methods to overcome the one-sidedness of a single weighting method. Besides, we resort to mutual information to determine a more reasonable index weight by eliminating the possible information overlap among indicators. The evaluation results of the simulation case demonstrate the effectiveness of the proposed approach for green construction evaluation.

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26. An Extended Grey Bass Diffusion Model With Dynamic Market Capacity

Xiansheng Fan, Zhengxin Wang, Lingling Pei

The Journal of Grey System 2023, 35 (3): 71-81.

摘要（125）

The structure of the classical Bass diffusion model reveals that the maximum number of imitators is achieved when the cumulative number of adopters equals half the maximum number of adopters in the market. But this situation does not necessarily correspond to the actual activities. To more accurately represent where the number of imitators reaches its peak, a new grey Bass diffusion model for cases with small samples is proposed by introducing a parameter to the classical Bass diffusion model to improve the model. In addition, the solution of the grey Bass diffusion model is derived by integrating the grey Bass diffusion model representation, and the parameter-solving process of the new grey Bass diffusion model is given by using the ordinary least squares method. Finally, an example of new energy vehicle sales forecasting shows that the new grey Bass diffusion model is more accurate than the traditional grey Bass diffusion model. The new grey Bass diffusion model further broadens the use of the Bass diffusion models and enriches the mathematical methods of innovation diffusion.

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27. Forecasting New Energy Vehicle Sales in China Based on a Novel Grey Lotka-Volterra Model and Assessing Its Environmental Impact

Wuyong Qian, Tingting Zou, Yuhong Wang, Chunyi Ji, Minghao Ran

The Journal of Grey System 2023, 35 (3): 82-99.

摘要（205）

With China's vigorous implementation of the two-carbon policy, the automotive industry is transitioning from traditional to alternative energy sources. Accurate forecasting of new energy vehicle sales can provide statistical support for policy planning. This paper proposed a grey Lotka-Volterra model based on an HP filter to forecast new energy vehicle sales trends. The proposed model overcomes the limitations of the original model in forecasting cyclical data and improves its applicability in small sample data systems. And the competitive forecasting model allows us to explore the market competition or cooperation between various vehicle types. Compared to the two existing models, the new model performs better in forecasting vehicle sales. The study further applies the LCA method to assess the scale of energy consumption and GHG emissions in the automotive sector. The prediction and evaluation results show that new energy vehicle sales will surpass traditional fuel vehicles by 2035 and dominate the vehicle market before 2050. Unfortunately, vehicle electrification has not significantly reduced the transportation industry's environmental concerns. To fully utilize the potential for energy-savings and emission-reduction of new energy vehicles, it is urgent to pursue technological advancements in battery production and power-generating structure.

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28. Grey Clustering Evaluation of the Science and Technology Innovation Platform Considering Technology Readiness Level

Huyi Zhang, Lijie Feng, Jinfeng Wang, Kuoyi Lin, Tiancong Zhu

The Journal of Grey System 2023, 35 (3): 100-116.

摘要（154）

Technological innovation is the primary driving force leading development. The science and technology innovation platform is important for enhancing innovation capabilities. Aiming at the operational performance of the science and technology innovation platform, it can be evaluated through the technology readiness level and the grey clustering evaluation model. First, we take the technology readiness level as the entry point to divide the science and technology innovation platform. On this basis, the operation evaluation index system of the science and technology innovation platform is constructed. After that, we construct the grey clustering evaluation model and conduct a case study to verify the feasibility of the study. Finally, we focus on the evaluation indicators and put forward relevant reference suggestions to improve the operational performance of the science and technology innovation platform.

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29. Research on the Supply and Demand Matching of Care Services for Disabled Elderly Individuals in the Community

Yun Fan, Jun Liu, Na Zhang, Zhigeng Fang, Sifeng Liu, Xiaojun Guo, Xin Lin, Zhihao Huang

The Journal of Grey System 2023, 35 (3): 117-138.

摘要（192）

To address the unreasonable matching of care service resources for disabled elderly individuals in the community, we first identified uncertainties in the expression of care needs by disabled elderly individuals and their families and the expression of care service resources by care institutions, defined the matching of the supply and demand of care service resources for disabled elderly individuals, and explored the expected demand evaluation values of different types of disabled elderly individuals and care service institutions. A grey bilateral matching model for care service resources in the case of incomplete supply and demand information was then constructed by considering the different degrees of disability of disabled elderly individuals, extending from the original one-to-one matching model to a one-to-many matching model. Finally, MATLAB simulation was used to obtain the optimal match between disabled elderly individuals and care service institutions, thereby providing an accurate and efficient match between the supply and demand of care service resources.

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30. A Contribution-based Model for Space Launch Systems Allocation

Fei Deng, Sifeng Liu, Luyun Qiu, Huan Wang, Yingjie Yang

The Journal of Grey System 2023, 35 (3): 139-156.

摘要（82）

Cost allocation is a critical part of the space launch system R&D stage of cost control. There exists a central challenge that the efficiency (also called input-output ratio) is difficult to obtain due to the uncontrollable input, long R&D cycle, and unpredictable output. Therefore, in order to obtain effective cost allocation strategies in practice, this paper proposes an improved contribution-based cost allocation method according to the measurable contribution of each team, bypassing calculating the uncertainty efficiency. First, a grey relational clustering-based evaluation system is developed to assess the contribution of the R&D team. Then, the real circumstances are examined, and four popular categories of launch tasks are identified. Next, the BWM method is employed to identify cost allocation strategies that align with the requirements of each of the four launch missions. Finally, comparative analyses with DEA and Costing method demonstrate the superiority of the proposed method in terms of accuracy and efficiency.

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31. 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.

摘要（144）

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.

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32. Grey Clustering Methods With Universal Possibility Functions

Long Wang, Zhigeng Fang, Qin Zhang, Sifeng Liu

The Journal of Grey System 2023, 35 (4): 19-33.

摘要（125）

The traditional possibility functions are always assumed to be linear functions. The preferences of decision-makers are not considered. It might not be proper to analyze all kinds of indicators with the traditional possibility functions. Therefore, we consider the preferences and first develop the universal possibility functions. The decision-makers can obtain the appropriate universal possibility functions by adjusting the clustering preference. Then, the related properties are revealed by the proof. Next, grey clustering methods with universal possibility functions are proposed. Finally, the effectiveness of the suggested methods is verified via the case illustration and comparative analysis.

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33. An Exponential-Polynomial Matrix Model Based on the Accumulation Generation of Ternary Interval Number Series and Its Application in Forecasting China's GDP by Region

Lihua Ning, Fangli He, Xiangyan Zeng, Yunjie Mei, Haoze Cang

The Journal of Grey System 2023, 35 (4): 34-54.

摘要（179）

Ternary interval number includes the total GDP amount in a certain period and its change range. Comprehensive information is more conducive to management decision-making. Affected by regional characteristics and national macro-control, the development trend of GDP in various regions of China in the past 15 years has been different. Some central regions grew rapidly in the early stage and fell back in the later stage, showing a saturated growth trend. Some coastal economically developed areas showed exponential growth. While some regions show an unstable upward and downward fluctuation trend. In order to predict the development trend of different GDPs, a matrix model based on exponential and polynomial regression, which can directly model the ternary interval number, is proposed in this paper. In order to eliminate the random fluctuation of data, the original ternary interval number sequence is accumulated based on the data preprocessing method in the grey model, which makes the general non-negative sequence show quasi-exponential growth so that it can be applied to the exponential-polynomial matrix model. The particle swarm optimization algorithm and the least square method are combined to estimate the parameters of the new model. The new model, quadratic polynomial, GM (1, 1), and exponential function are used to predict the GDP of 31 regions in China from 2005 to 2020. The results show that the effect of the new model is better than other models in predicting GDP for 20 regions.

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34. A Novel Modeling Method of Extended Grey EGM(1,1,∑e^(ck)) Model and Its Application in Predictions

Maolin Cheng, Bin Liu

The Journal of Grey System 2023, 35 (4): 55-75.

摘要（128）

In the grey models, the GM(1,1) model is an important type of prediction model. The traditional grey GM(1,1) model has good prediction results in the case the original data show exponential variations at a slow rate. However, in practical problems, although showing exponential variations or approximately exponential variations, original data vary very fast sometimes. In these cases, the traditional grey GM(1,1) model tends to have poor prediction accuracy, mainly because the data fails to meet the laws presented by the traditional model. Therefore, the paper makes improvements in the following two aspects: first, the paper transforms the traditional accumulated generating sequence of original data; second, the paper extends the traditional grey model's structure, i.e., building a grey EGM(1,1,∑e^(ck)) model. The paper offers the parameter optimization method of the grey EGM(1,1,∑e^(ck)) model. Using the novel modeling method proposed, the paper builds the grey EGM(1,1,∑e^(ck)) models for China's total electricity consumption and China's GDP per capita, respectively, in the final section. Results show that the models built with the proposed modeling method have high simulation precision and prediction precision.

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35. A Multi-attribute Decision-making Method Based on Grey Correlation

Lirong Sun, Chi Zheng, Chenkai Jiang, Yinghua Tian, Yujing Ye

The Journal of Grey System 2023, 35 (4): 76-90.

摘要（189）

Aiming at the grey feature problem of ' small sample and poor information ', this paper extends the traditional analytic hierarchy process, entropy method and ' vertical and horizontal ' scatter degree method to the field of grey number, and proposes a multi-attribute decision-making method based on grey correlation. Firstly, the applicable form of index weight is enriched, and the determination method of index weight in grey number form is given systematically. Secondly, aiming at the problem that the traditional evaluation method can not be directly applied to the comprehensive evaluation with grey characteristics, a comprehensive evaluation model in the form of grey number is proposed. Finally, through the interval grey number integration method and the ' kernel and grey number ' integration method, the evaluation values under each index are formed into a comprehensive evaluation value, and the evaluation results are sorted. Compared with the traditional evaluation method, the proposed method more reflects the rationality and dynamics of the evaluation results.

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36. 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.

摘要（120）

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.

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37. 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.

摘要（146）

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.

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38. 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.

摘要（263）

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.

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39. Improved Fractional Order Single Optimization Parameter Grey Model

Jiangtao Wei, Yonghong Wu

The Journal of Grey System 2023, 35 (4): 154-171.

摘要（360）

Some grey prediction models suffer from outliers and overfitting, and their prediction performance can be improved. Based on the fractional grey model (FGM) and the fractional time delayed grey model (FTDGM), an improved fractional single optimization parameter grey model (IFSGM) is proposed in this paper. A timetranslation power term is used to reduce model overfitting. The data is pre-processed to reduce the influence of outliers based on data transformation in cumulants and summations. The convolutional computational formulation is used to perform the prediction and improve the prediction effect. The genetic optimization algorithm is used to optimize the order of the fractional cumulants, find the optimal value of the order, and improve the model fit and prediction effect. In 6 data sets, the IFSGM and the 7 grey models are compared and tested. The experimental results show that IFSGM achieves excellent prediction performance.

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40. On Grey Weighted Central Moving Average Model and Its Application

Sifeng Liu, Zurun Xu, Liangyan Tao, Yingjie Yang

The Journal of Grey System 2023, 35 (4): 172-182.

摘要（112）

The idea and method of weight vector group of kernel clustering have been combined with the central moving average model and grey system prediction model in response to the problems existing in the traditional moving average formula. A grey-weighted central moving average model was proposed in this paper. In the modeling process of the grey-weighted center moving average model, the number of moving average terms should be determined first, and the weight vector should be set according to the rules of weight setting for each component of the weight vector group of kernel clustering. Next, the weighted center moving average formula can be used to calculate the moving average simulation value, and the simulation errors were analyzed. Then, the grey system prediction model is applied to obtain a set of predicted values for the studied time series data. Finally, based on actual data and the predicted values of the grey system model, the required predicted values are calculated using the weighted center moving average formula. The new model can effectively solve the problem of serious lag in the simulation and prediction results of the simple moving average formula and the weighted moving average formula and also overcome the shortcomings of the center moving average model and the weighted center moving average model, which cannot be used to predict future changes due to the need for data on both sides of the "center" yt during calculation. From the simulation and prediction results of China's invention patent authorization volume, it can be seen that the new model has obvious advantages.

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