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    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.  
    Abstract62)           
    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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    A Novel EGM(1,1) Model Based On Kernel And Degree Of Greyness And Its Application On Smog Prediction
    Hui Shu, Pingping Xiong, Shiting Chen
    The Journal of Grey System    2020, 32 (4): 1-14.  
    Abstract2036)           
    The task of smog control in China is still arduous compared with developed economies. To address the problems associated with the uncertain of smog pollution, this paper establishes a new EGM (even grey model) (1,1) prediction model based on the kernel and degree of greyness under the condition that the possibility function is known. The original EGM(1,1) prediction model based on the interval grey number sequence is constructed under circumstances where the possibility function is unknown. For testing the proposed model, the daily AQI data of Nanjing, Jiangsu Province, China, was selected. Also, this paper uses another five forecasting models and compares the results with the new model. The results show that the daily AQI index of Nanjing presents a significant downward trend excluding seasonal factors, and the prediction accuracy of the new EGM (1,1) model is also higher than that of other forecasting models.
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    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.  
    Abstract302)           
    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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    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.  
    Abstract250)           
    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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    Fresh-keeping Strategy of Agricultural Products Supply Chain Considering Grey Game
    Qing Zhang, Qiuyu Zhang, Zhichao Zhang
    The Journal of Grey System    2020, 32 (3): 1-10.  
    Abstract856)           
    This paper uses grey number to identify the freshness degree of agricultural products. A contract to share profits between the farmer and the retailer is established based on their fresh-keeping efforts and we build their profits model respectively. We use game theory based on grey matrix to analyze their fresh-keeping strategy and get conclusions through numeric example: the retailer tends to take measures to keep products fresh whatever the farmer’s decision while the farmer’s fresh-keeping strategy is influenced by the proportion of profits-sharing. In given conditions, when we set the proportion a specific set, we can find a Nash equation. The result shows that in the end both the farmer and the retailer will keep products fresh.
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    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.  
    Abstract335)           
    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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    Relevance of Quality Infrastructure with Promoting Export Quality: Evidence from Emerging Markets
    Mengdie Huang, Tangbin Xia, Hao Zhang, Ershun Pan, Lifeng Xi
    The Journal of Grey System    2020, 32 (4): 32-51.  
    Abstract215)           
    With the increase of global trade and sourcing, there is a growing need for exact measurement and reliable standards for products and services. This paper attempts to develop a unified and integrated structure for the effectiveness evaluation of quality infrastructure on the promotion of export quality from the perspective of system and coordination. Starting from determining component-based evaluation criteria and index, we propose a three-phase analytical framework. Firstly, the development level of quality infrastructure system is evaluated through factor analysis. Secondly, the coordination degree of quality infrastructure system is calculated by grey coordination evaluation model. Thirdly, we explored the relevance of quality infrastructure system within export quality through grey relational analysis. Using a sample of quality infrastructure and export data from 2009 to 2018 in China, empirical results show that quality infrastructure can be divided into two subsystems according to their characteristics including 'scale and structure subsystem' and 'standard subsystem'. There is evidence that the performance of a quality infrastructure system and its coordination degree are closely related to the upgrade of export product quality. The main contribution of this paper is to address the gap in the quality infrastructure literature by proposing a three-phase analytical framework for effectiveness quantification problems. The clarification of the economic connection between quality infrastructure and export product quality can raise awareness of governments and enterprises about the significance of construction and utilization of quality infrastructure system for competitive advantages.
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    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.  
    Abstract268)           
    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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    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.  
    Abstract192)           
    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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    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.  
    Abstract193)           
    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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     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.  
    Abstract249)           
    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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    Defective Recognition with MTD-based Non-Equigap Grey Models
    Yao San Lin, Der-Chiang Li, Chien-Chih Chen, Hung-Yu Chen
    The Journal of Grey System    2020, 32 (3): 11-20.  
    Abstract181)           
    The TFT-LCD (thin-film transistor liquid crystal display) industry in Taiwan has been developed for decades. To provide better service for customers, most Taiwan companies in the supply chain have set up their warehouse in mainland China for vendor managed inventory (VMI). However, over the last decade, owing to the industry issues of product diversity strategies and short product lifecycles, it has become difficult for suppliers to control well the stock level in VMI, especially the operation of defective product returns. In order to keep high customer satisfaction, it is considered an option by forecasting possible future defectives for preparing the returning products to satisfy customers. The non-equigap grey model (NGM) used to be applied to such short-term time series data and has shown to be an effective tool. However, NGM predictions still can be improved by making more appropriate background values by determining their parameter α values. Accordingly, this paper employs the mega-trend-diffusion (MTD) technique to estimate better α values, and the model is thus called MTD-NGM(1,1). In the experiments, two data sets taken from a supplier are examined for effectiveness validation. The experimental results indicate that MTD-NGM(1,1) can generally produce better predictions than NGM(1,1).
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    Grey Incidence Model for Multivariate Time Series with Different Length based on Spatial Pyramid Pooling
    Ke Zhang, Yao Yin, Le Cui
    The Journal of Grey System    2020, 32 (3): 48-59.  
    Abstract133)           
    Aiming at the problem that existing multivariate grey incidence models can not be applied to different length multivariate time series (MTS), a new model was proposed based on spatial pyramid pooling (SPP). Firstly, the local features of an MTS with different lengths were pooled and aggregated by SPP to construct feature pooling matrices on the same size. Secondly, classic multivariate grey incidence models were used to measure the degree of incidence between feature pooling matrices. Finally, the effectiveness of the models was verified on two data sets compared with a variety of algorithms.
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    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.  
    Abstract257)           
    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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    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.  
    Abstract150)           
    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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    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.  
    Abstract217)           
    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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    A Variable Selection Method for GM(1,N) Model
    Dang Luo, Xiaolei Wang, Yimeng An
    The Journal of Grey System    2020, 32 (4): 119-136.  
    Abstract224)           
    Variable selection is the basis of GM(1,N) model, and also one of the key factors that affect grey model performance. Based on the adaptability between actual data and theoretical model, this paper recognizes the parameter estimation of grey model as a general linear model and discusses the effect of variable selection on parameter estimation and prediction performance. It is proved that discarding those relevant variables which have little influence is helpful to improve the modeling accuracy. Then, a variable selection method for GM(1,N) model under RMS, R2 and AIC criteria is proposed, and the calculation order and calculation method are given. Finally, the method is applied to predict the agricultural drought vulnerability in Xinyang City, Henan Province. The results show that the method not only identifies the main influencing factors of drought vulnerability but also further improves the prediction accuracy
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    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.  
    Abstract229)           
    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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    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.  
    Abstract185)           
    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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     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.  
    Abstract142)           
    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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