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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.   Abstract （302）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （856）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （334）            Knowledge map    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 Related Articles | Metrics

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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.   Abstract （257）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （193）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （2036）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （268）            Knowledge map    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. Related Articles | Metrics

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Multi-attribute Group Grey Target Decision-making Method Based on Three-parameter Interval Grey Number Ye Li, Dongxing Zhang The Journal of Grey System    2020, 32 (3): 96-109.   Abstract （201）            Knowledge map    Considering the value information of the three-parameter interval grey number and the risk attitude of decision-maker, a multi-attribute group grey target decision-making method based on a three-parameter interval grey number is advanced. Firstly, the nonlinear averaging operators are constructed to reflect the risk attitude of decision-makers. Then, the definition of the relative kernel and distance measure of the three-parameter interval number is given while considering the value characteristics. Next, the positive and negative clouts of the schemes are determined by the size of the grey number's kernel and the degree of accuracy, and two models are constructed based on the principle of maximum relative off-target distance and grey entropy to determine the weights of attributes and decision-makers. And then, the relative off-target distance of positive and negative off-target distance is used to rank and optimize the schemes. Lastly, an example is delivered to illustrate the rationality and feasibility of the proposed method. Related Articles | Metrics

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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.   Abstract （229）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （250）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （192）            Knowledge map    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. Related Articles | Metrics

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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.   Abstract （181）            Knowledge map    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). Related Articles | Metrics

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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.   Abstract （215）            Knowledge map    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. Related Articles | Metrics

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A Graph model for Conflict Resolution based on a Grey Multi-criteria Preference Ranking Approach Jian Li , Wanming Chen , Huanhuan Zhao , Renshi Zhang The Journal of Grey System    2021, 33 (2): 109-127.   Abstract （228）      PDF （368KB）（400）       Knowledge map    Preference ranking is a vital issue in the process of graph model for conflict resolution (GMCR). Concerning the ranking problem of uncertainty preference, we propose a grey multi-criteria preference ranking approach based on grey interval numbers to represent the uncertainty preference of decision-makers, and calculate the comprehensive grey incidence degrees between DMs. And then, based on maximum entropy, we construct a multi-objective optimization model to minimize uncertainty. Finally, we exploit a real-world conflict incident of "Taihu Lake water pollution" to illustrate the feasibility and effectiveness of the proposed model Related Articles | Metrics

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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.   Abstract （217）            Knowledge map    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. Related Articles | Metrics

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Taylor Series approximation based Unbiased GM(1,1) Hybrid Statistical Approach for Forecasting Stock Market R. M. Kapila Tharanga Rathnayaka, D. M. K. N. Seneviratna The Journal of Grey System    2020, 32 (3): 124-133.   Abstract （190）            Knowledge map    Due to the volatility with unstably in the modern finance, the ability of forecasting is notoriously embarrassing and represents a major challenge with traditional time series forecasting methods; especially, most of the available approaches are still weak to forecast future predictions under the unbalanced frameworks. The purpose of this current study is to propose a Taylor Series approximation based Unbiased GM(1,1) Hybrid approach (HTS_UGM(1,1)) to handle incomplete, noise and uncertain data in multidisciplinary systems. Related Articles | Metrics

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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.   Abstract （224）            Knowledge map    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 Related Articles | Metrics

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Identifying the Influencing Factors of Patient’s Attitude to Medical Service Price by Combing Grey Relational Theory with CMH Statistical Analysis Chongxu Zhang, Lizhong Duan, Hangyu Liu, Yinran Zhang, Lili Yin, Qi Lu, Guna Duan The Journal of Grey System    2020, 32 (3): 80-95.   Abstract （179）            Knowledge map    The purpose of the paper is to explore the influencing factors of the patient’s attitude to the medical service price. Literature analysis and expert interviews are used to design the questionnaire. Using a convenient sampling method to extract 600 patients from the five areas of Beijing, Tianjin, Hebei, Shandong and Liaoning. Combing grey relational analysis with Cochran-Mantel-Haenszel (CMH) statistical analysis to explore the influencing factors of the attitude in the medical service price. The results show that region, gender, age, education, professional title, income by month, medical insurance, commercial medical insurance and work unit are related to the distribution of patients’ attitude of medical service price by CMH statistical analysis. The sorting of Grey relational grade is Region (0.997)> Gender (0.939)> Commercial Medical Insurance (0.828)> Level of Medical institution (0.736)> Income by month(RMB) (0.701)> Medical insurance (0.644)> Professional Title (0.598)> Work unit (0.545)> Age (0.481)> Education (0.462); The grey relational grade of those respondents surveyed who are living in Shandong province (0.821), female (0.797), don’t buy commercial medical insurance (0.846), go to the tertiary hospital lately (0.831) and have income of 4000-6000 yuan by month (0.840) are higher than others. The current medical service price is higher than the reasonable level, especially in the operation fee and examination fee involving large consumables. The patient’s satisfaction with the price of medical service items is different in different variables, and the main influencing factors are as follows: Region, Gender, Commercial Medical Insurance, Level of Medical institution and Income by month (RMB). Related Articles | Metrics

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A novel grey model for multi-regional macro-data forecasting by considering spatial correlation and actual-state rolling Ying Zhu, Yaping Li, Tangbin Xia, Lifeng Xi The Journal of Grey System    2021, 33 (2): 14-28.   Abstract （235）            Knowledge map    Accurate prediction of regional development trend is important to regional planning and coordinated development in China. It provides a basis for decision-makings on the resource balance in multi-regional integration. However, due to the limitation of macro data and the influence of multi-regional correlation, the prediction accuracy of the existing forecasting methods in multi-regional macro-data forecasting is reduced. To overcome these problems, an improved grey model is proposed in this study. Firstly, a new spatial weight matrix is constructed based on the grey correlation analysis to define the spatial effect of multiple regions. Then, an actual-state rolling spatial-effect weighted grey model (ARSWGM) is developed considering the spatial interactions and the actual-state rolling mechanism. Finally, the proposed model is validated by the forecasting of manufacturing quality level of representative provinces in the process of regional coordinated development in China. The result shows that the proposed model demonstrates the best predicting performance compared with the classical grey forecasting models, indicating the advantages of this proposed model in multi-regional macro-data forecasting. Furthermore, this model can also be applied for a broader range of multi-regional limited macro-data forecasting. Related Articles | Metrics

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Grey System Model with Complex Order Accumulation Zhengpeng Wu, Jianke Chen, Jianping Chai, Fangyuan Zhang The Journal of Grey System    2021, 33 (1): 98-117.   Abstract （6636）            Knowledge map    Based on the classical GM(1,1) model of integer (fractional) accumulation, we propose the grey model of complex accumulation (which is denoted by CAGM z(1,1) for some complex number z ∈ C ). This formulation extends the choice of Grey model's parameter from the real axis to the complex plane. We claim that all complex accumulated generating operators admit a1 dimensional additive complex Lie group's structure, which is isomorphic to C. This construction brings Lie group's theory in Grey model theory for the first time, and lays a foundation for introducing Lie group's tools in the grey system. The method of nilpotent matrix E1 of index n and Taylor series could avoid any usage of existing popular Γ functions, which also provides an efficient way for computer programming. As a novel method, accumulated generating operators of complex order could adjust weights between old information and new information, between the real part and the imaginary part simultaneously, better simulation and prediction results could be expected. The advantages of CAGM z(1,1) model are discussed with several cases, better simulation and prediction results are presented. Related Articles | Metrics