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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.  Evaluation and Analysis of Smart Community Elderly Care Service Quality Based on the Two-stage Decision Model with Contents Grey Synthetic Measures under Hesitant Fuzzy Situation
    Lan Xu, Yu Zhang, Yeli Wei
    The Journal of Grey System    2021, 33 (1): 118-137.  
    摘要378)     
    To ensure smart elderly care service quality, this paper explores its multi-dimensional factors, and constructs an evaluation indicator system of smart community elderly care service quality based on intelligence, tangibles, responsiveness, security, reliability, and empathy. Aiming at the problem of the fuzziness of elderly's perception and the hesitation of experts’ evaluation of service quality in multi-attribute decision-making, the interval-valued intuitionistic fuzzy entropy (IVIFE) is introduced, and the evaluation method of the smart community elderly care service quality by combining the IVIFE and a two-stage decision model with grey synthetic measure is established. Four typical cities in Jiangsu Province were taken as examples to verify the feasibility of the proposed method, in order to provide a reference for promoting service standardization and reducing the difference in the level of smart community elderly care services between regions.
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    3.  GRGAL: A Grey Relational Generative Adversarial Learning Method for Image Denoising#br#
    Hongjun Li, Chaobo Li, Wei Hu, Junjie Chen, Shibing Zhang
    The Journal of Grey System    2021, 33 (1): 30-42.  
    摘要252)     
    Image denoising is a well-known problem in image processing. Deep networks can achieve state-of-the-art denoising results based on the quality or quantity of training samples. However, Deep networks face performance saturation when the interference of complex noise and few paired training samples. We introduce a grey relational generative adversarial learning method into the image denoising task. To solve the problem of deep network saturation caused by complex noises and the lack of paired training samples, an adversarial learning network is built to learn latent space distribution of noisy images and reconstruct the distribution of clear images. The grey relation analysis is introduced into the network to deal with the uncertainty of noisy images and improve the ability of adversarial learning. This network is optimized by a new loss function that combined the adversary and grey relation. The loss can reasonably measure the difference between the denoised images and clear images. Experiential results show the proposed method obtains the averaged PSNR of 29.67, which is 0.53 higher than the network without grey relation. Extensive experiments demonstrate the superiority of our approach in image denoising.
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    4. Relationship Between Pore Structure And Bending Strength Of Concrete Under A High-Low Temperature Cycle Based On Grey System Theory
    Jinna Shi, Yanru Zhao, Bo Zeng
    The Journal of Grey System    2020, 32 (4): 101-118.  
    摘要408)     
    In the area where the temperature changes dramatically, the concrete pavement is affected by high and low temperature for a long time, which changes its internal pore structure and finally leads to the decline of the concrete mechanical properties. Many scholars have studied the relationship between strength and porosity of concrete. Nevertheless, for conclusive findings, a large amount of experimental data is required; otherwise, it is challenging to draw reliable statistical conclusions. For concrete, the properties of raw materials, the production technology, the measuring process of strength and the accuracy of equipment are all uncertain. Multiple uncertainty factors not only contribute to an insufficient amount of experimental data but also inaccuracy. In the current study, in the light of small data samples, the model of total porosity and bending strength of concrete is established based on grey system theory. When compared with other models, it reports a lesser error. By studying the interactions among the pore sizes and the influence on the bending strength, the model is further improved. The average relative error is only 1.63%. The proposed methodology provides an analytical basis for the study of the relationship between pore porosity and bending strength of pavement concrete under temperature fatigue in the area with a large temperature difference. It also provides a specific reference for establishing the relationship model between variables in the case of a small amount of data
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    5. A Fuzzy-based Approach for Improving Accuracy of Grey Forecasting Models
    Tung-I Tsai, Chun-Wu Yeh, Liang-Sian Lin, Che-Jung Chang, Der-Chiang Li
    The Journal of Grey System    2020, 32 (3): 21-33.  
    摘要260)     
    Over the past two decades, the grey model (GM) and its extensions have shown to be an effective tool to deal with short-term time series (STTS) data. To further improve the accuracy of GM models, this paper proposes a novel GM modelling procedure based on a fuzzy-set concept. In the procedure, STTS data is fuzzified by measuring the forces between existing data and a newly coming datum to form fuzzy time series for building GM models, and final predictions are defuzzified by aggregating the predictions of the GM models with the proposed weights. The experimental results of a real case indicate that the proposed procedure can further improve the accuracy of GM models in general.
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    6. 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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    7. Risk-transmission Mechanism of Industry Chain under a Multi-parameter Grey-GERT Network
    Lan Xu, Yingying Shang
    The Journal of Grey System    2024, 36 (3): 63-73.  
    摘要133)     
    Aiming at the risk of local obstruction or rupture in the operation process of the industry chain, a Grey-GERT network model of industry chain risk transmission is constructed based on the effect of input resources of each link of the industry chain, and the key links and their degree of risk in the process of industry chain network value transmission are identified and analysed to reveal the risk transmission mechanism of the industry chain. Finally, an empirical study is conducted on China’s integrated circuit industry chain to verify the feasibility and effectiveness of the proposed model and to propose targeted control measures for the key links and their value transmission risks. The results show that the proposed model can effectively solve the problem of incomplete information on multiple transmission parameters in industry chain network activities, thoroughly analyse the risk transmission mechanism of the industry chain, and provide theoretical support for strengthening the risk control of the industry chain.
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    8. Analysis of Eco-Efficiency in China's Key Provinces along the “Belt and Road” Based on Grey TOPSIS-DEA
    Fanlin Meng, Wenping Wang
    The Journal of Grey System    2020, 32 (3): 60-79.  
    摘要236)     
    Under the background of "Green Belt and Road", exploring the transition path from "high energy consumption and high pollution" to green development in regions along the “Belt and Road" is of great significance for achieving the healthy and sustainable development of the economy. The current study decomposes the industrial eco-economic system into manufacturing subsystems and environmental protection subsystems, separately establishes the eco-efficiency evaluation index system of the two subsystems, and introduces the grey system theory’s "small sample and poor information" uncertainty problem into the TOPSIS-DEA cross- efficiency model to construct Grey TOPSIS-DEA model to measure the eco- efficiency of China’s key provinces along the "Belt and Road" from 2005 to 2016. On this basis, this paper analyzes the differences in the contribution rate of production factor to eco-efficiency growth in various regions. The results show that: the eco-efficiency of the whole industrial eco-economic system and the manufacturing subsystem of China's key provinces along the "Belt and Road" presents a general downward trend, with a slight fluctuation in the middle, and the eco-efficiency of the "One Belt" regions is lower than that of the "One Road" regions. The eco-efficiency of environmental protection subsystems in most regions along the line shows an increasing trend, and it is significantly lower than that of the industrial eco-economic system and the manufacturing subsystem. In addition, for High Manufacturing-High Environmental Protection areas, the contribution of labor to the improvement of eco-efficiency is the largest, and for other three types of areas, capital plays the most crucial role in improving eco-efficiency.
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    9. Using Improved Non-linear Multivariate Grey Bernoulli Model to Evaluate China's CO2 Emission
    Cholho Pang, Decheng Fan, Jongsu Kim, Yonsun O
    The Journal of Grey System    2020, 32 (4): 15-31.  
    摘要310)     
    The current study proposed the improved non-linear multi-variable Grey Bernoulli model and predicted the CO2 emissions in China. Firstly, the paper presents an improved multivariate grey Bernoulli model (INGBM(1, N)) that considers the nonlinearities of the system characteristic data and related factors in establishing the grey model. Secondly, the influence of the relevant factors on the grey model's forecast accuracy has been considered. The more the number of relevant factors, the higher the relative level with the system characteristic data, the higher the calculation accuracy. However, predictive accuracy began to decrease again after the number of relevant factors more than a specific value. Thirdly, we selected the number of relevant factors as 4 (coal energy consumption, urbanization rate, crude oil, population) and carried out compared analysis with other grey models and non-grey models. The results show that the proposed model has the best forecasting accuracy. The proposed model is a generalization of several other grey forecasting models. China's CO2 emissions for 2019-2021 is forecasted. It estimated that the value would continue to increase over the next three years and reach 9958.57Mt by 2021. Finally, several measures have briefly mentioned reducing CO2 emissions based on the influence of relevant factors.
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    10.  Grey Exponential Cloud Decision Model for Monotonic Hesitant Fuzzy Linguistic Terms
    Yuan Liu, Zhuozhuo Yang, Jinjin Zhu, Jingjing Hao, Xinwang Jiang
    The Journal of Grey System    2021, 33 (1): 1-16.  
    摘要269)     
    Monotonic natural language is widely used to express experts' subjective appraisal opinions, such as "not less than," "at least," "not more than," and "at most," which covey the information of expert hidden psychological preference. A novel quantitative computational method based on the grey exponential cloud model is proposed, transforming the expert's uncertainty appraisal information into decision data by systematically mining the experts' hesitant fuzzy preference on specific linguistic options. The comprehensive meaning of monotonic hesitant fuzzy linguistic terms is introduced, and the interval grey number is used to represent the expert's grey preference and indicator weight. Additionally, a programming model is constructed by the exponential cloud model and ABC classification analysis method, which can obtain the order of alternatives related to the optimal solution. Finally, a numerical study is conducted to show the advantages and effectiveness of the new method against other comparable methods is demonstrated.
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    11. Research on Improved GM (1,1) Model Based on Optimization of Initial Item and Background Value
    Yuhong Wang, Jie Lu
    The Journal of Grey System    2020, 32 (4): 137-146.  
    摘要281)     
    Grey prediction theory is an important part of grey system theory. As one of the important models of grey prediction theory, GM (1,1) model has been widely used in economy, management, energy and other fields. In order to improve the prediction accuracy of the classical GM (1,1) model, this paper proposes a combined optimization method, that is, the difference equation is used to replace the static equation in the classical model, and the variable weight is used to construct the background value to reduce the system error caused by human intervention. Taking the domestic soybean annual consumption data as an example, the validity of the combined model is verified. The results show that the prediction accuracy of the combined optimization model is significantly better than that of the classical GM (1,1) model.
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    12. Forecasting Realized Volatility in A Heterogeneous Market: A GM(1,1) Approach
    Xiaojun Chu, Qiang Huang, Guo Wei
    The Journal of Grey System    2020, 32 (4): 90-100.  
    摘要281)     
    In this study, a GM(1,1)-RV model is proposed to forecast the realized volatility. The heterogeneity of investor with different time horizons is taken into account. Unlike previous studies that used linear regression models, GM(1,1) is employed to model weekly or monthly realized volatility trend based on only 5 or 22 data. The empirical results based on Chinese stock market are demonstrated that the GM(1,1)-RV model can generate better forecasting performance than widely used HAR-RV-type regression models from statistical viewpoint and economic perspectives.
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    13. Grey Target Group Decision Model Based on Expected Intervals of Experts
    Xudong Xie, Mingli Hu, Yingjie Yang, Yuwen Zhang
    The Journal of Grey System    2020, 32 (4): 77-89.  
    摘要406)     
    In group decision-making, the behavior expectation of the relevant experts has a significant impact on the selection result of the group decision-making. To address this challenge, a grey target group decision-making model based on expert's expectations was proposed. The article considers the expert's expectations based on the distance between the expert's expected interval of each index and the average (bull's-eye), and the expert weights are derived from their expected interval. The value matrix is then normalized for the degree of interval coincidence between the expert's evaluations and his/her expected interval for the index. Finally, the paper proves the validity and feasibility of the proposed method through a case comparison analysis.
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    14. A Case-based Grey Relational Analysis Model for Multiple Criteria Classification of Thyroid Nodules
    Hongjun Sun, Feihong Yu, Haiyan Xu, Houxue Xia
    The Journal of Grey System    2020, 32 (4): 65-76.  
    摘要311)     
    Multi-criteria Decision Aiding (MCDA) paradigm has been utilized in solving classification problems. In this study, a novel MCDA classification method using case-based grey relational analysis (GRA) is proposed to solve the problem of classifying and diagnosing thyroid nodules. After a set of appropriate criteria are identified and qualified, representative cases are selected as input. Weighted distance based on GRA is defined to express the decision maker's preference. Then a quadratic optimization program is constructed to obtain optimal classification thresholds. This method can overcome the difficulties in the clinical diagnosis of thyroid nodules caused by the decision-maker's (DM) cognitive limitations. An experiment is conducted to demonstrate the procedure.
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    15. An Integrated Model Combining Grey Methods and Neural Networks and Its Application to Bursty Topic Tendency Prediction
    Yuling Hong, Qishan Zhang, Yingjie Yang, Ling Wu
    The Journal of Grey System    2020, 32 (4): 52-64.  
    摘要307)     
    Studying the development tendency of topics is an important part of the online social network (OSN) analysis. To solve the problems of ad hoc topic popularity, tendency prediction under insufficient samples, data sparsity and low accuracy of the prediction model, this study combines grey system theory with the neural network method to propose a new model for topic tendency prediction. In this study, the grey relational analysis method is used to construct the social network topic popularity evaluation index system, and the topic popularity tendency is classified and weighted based on the grey proximity, and then the integrated system combining GM(1,1) model with BP neural network (BP-NN) model is established. Taking Sina Weibo's bursty topic data as an example, the proposed model's effectiveness is verified. The experimental results show that the proposed hybrid methodology is better than a single independent prediction model and can be effectively used to predict the popularity of a social network topic.
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    16.  A Quality Overall Design Approach for Complex Products byintegrating Fuzzy QFD and Grey Relational Decision-making: A Quality Competitiveness Perspective
    Huan Wang, Daao Wang, Zhigeng Fang, Xiaqing Liu
    The Journal of Grey System    2021, 33 (1): 59-73.  
    摘要182)     
    This paper aims to propose a novel quality overall design approach for complex products. The core parameter design and scheme optimization in the perspective of quality competitiveness are deeply addressed. Integrating the fuzzy QFD approach and the grey relational decision-making model, this paper explores the uncertain analysis and multiple attribute decision-making problems for the quality overall design of complex products. The overall quality design of a civil aircraft is presented as a numerical example, and conclusions and future work are discussed.
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    17. A Remaining Useful Life Prediction Framework Integrating Multiple Time Window Convolutional Neural Networks
    Ya Song, Tangbin Xia, Yu Zheng, Bowen Sun, Ershun Pan, Lifeng Xi
    The Journal of Grey System    2020, 32 (3): 34-47.  
    摘要233)     
    Efficiently predicting Remaining Useful Life (RUL) of equipment is fundamental for assessing system health and developing maintenance strategies. Considering the high degree of inconsistency among the length of degradation trajectories, a multiple time window Convolutional Neural Networks (CNN) based framework is introduced to improve prediction accuracy. In this proposed method, one-dimensional CNN is adopted to learn degradation trends from historical sensor data, and a multiple time window strategy is exploited to reduce training errors and increase the utilization rate of test data. The performance of this proposed framework is validated through an experimental study and compared with state-of-the-art models. The comparison and analysis have demonstrated that this framework can achieve the best overall performance, and thus it can provide strong support for preventive maintenance.
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    18. 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.  
    摘要242)     
    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.
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    19. 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.  
    摘要238)     
    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.
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    20. 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.  
    摘要200)     
    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.
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