The Journal of Grey System

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

Zhaoya Zhang, Naiming Xie, Lu Yang, Xiaolei Wang

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

摘要（99）

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

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2. 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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3. 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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4. 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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5. 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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6. A Conformable Fractional Non-homogeneous Grey Forecasting Model with Adjustable Parameters CFNGMA(1,1,k,c) and its Application

Wenqing Wu , Xin Ma , Bo Zeng , Peng Zhang

The Journal of Grey System 2024, 36 (2): 1-12.

摘要（206）

The inconsistency between the whitening differential equation and the grey basic form of the non-homogeneous continuous grey model CFNGM(1,1,k,c) will result in internal errors. Thus this paper proposes a CFNGMA(1,1,k,c) model with adjustable parameters, which improves the accuracy of the CFNGM(1,1,k,c). This paper first elucidates reasons for the internal errors generated by the continuous grey model CFNGM(1,1,k,c), and explains the classic method, the discrete grey forecasting model, of eliminating internal errors. On the basis of an in-depth analysis of the modeling mechanism of CFNGM(1,1,k,c) model, a new parameter adjustable grey forecasting model is proposed by introducing parameter adjustment factors to modify model’s parameters. Finally, the new model is applied to explore the gross regional product of Chengdu and Deyang in the Chengdu metropolitan area. The calculation results indicate that the newly proposed model can obtain more accurate results.

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7. Reinforcement Model for Unmanned Combat System of Systems Based on Multi-Layer Grey Target

Xueting Hao, Zhigeng Fang, Jingru Zhang, Fei Deng, Ankang Jiang, Shuyu Xiao

The Journal of Grey System 2024, 36 (2): 54-66.

摘要（179）

In the future battlefield, unmanned combat mode will be crucial. Its attack strategy formulation is a significant and complex task. To address the issue of decisionmaking in unmanned combat system of systems(UCSoS) striking strategy, this paper begins by analyzing the characteristics of UCSoS. By utilizing the GERT concept, an unmanned combat A-GERT network is developed to provide parameter support for evaluating its effectiveness. Secondly, for effectiveness evaluation, a multi-layer gray target model built on the A-GERT network is proposed. This model is utilized to formulate the optimal striking scheme for the UCSoS. And Agent technology is employed to solve the intelligent learning decision-making problem for UCSoS based on multi-layer grey target model. Finally, a case study illustrates the efficiency and effectiveness of the reinforcement model for UCSoS based on multi-layer grey target.

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8. 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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9. 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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10. 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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11. 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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12. 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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13. 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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14. 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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15. 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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16. 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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17. 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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18. 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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19. 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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20. Interaction-based nonlinear INDGM(1,N) model and its application

Ye Li, Dongyu Liu, Junjuan Liu, Meidan Xiao

The Journal of Grey System 2024, 36 (1): 56-62.

摘要（152）

Multivariate grey models are commonly used to evaluate the independent effects of related factors, but they may fail to account for any nonlinear interactions that could exist between them. To address this limitation, this study introduces the INDGM(1,N) model, which considers the nonlinear interactions between related factors. Simultaneously, to depict the nonlinear impact of both the system behavior sequence and corresponding factor sequences more accurately, varying power parameters have been incorporated into the model proposed in this paper. Moreover, by adjusting the parameter values of the INDGM(1,N) model, it can be converted into several other models, such as the DGM(1,N) model, GM(1,N) model, DGM(1,1) model, or GM(1,1) model. This study uses a genetic algorithm to obtain the time response of the INDGM(1,N) model by solving its nonlinear characteristic parameters. We then use the model to simulate and forecast China's CO2 emissions and compare its performance with that of other models. The results show that the INDGM(1,N) model provides more accurate simulation and prediction accuracy than other models, highlighting its effectiveness.

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