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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

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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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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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A New Approach for Interval Grey Numbers: n-th Order Degree of Greyness Erdal Aydemir The Journal of Grey System    2020, 32 (2): 89-103.   Abstract （768）            Knowledge map    Uncertain information has complexity for various reasons in real-life decision-making problems in order to be useful information. Therefore, studying the characterization and size measurement of uncertain information is of significant interest. Therefore, the purpose of this paper is to investigate the n-th order level of the degree of greyness for analyzing as a new approach of distance measuring and sorting methods for general grey numbers. Also, a pseudocode form is given for the proposed method and illustrated by using an interval number, and its effects are presented on some experimental solutions Related Articles | Metrics

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Multi-attribute Grey Relational Similarity Measure Evaluation Method for Weapon System Performance Based on Entropyweight Wenguang Yang , Yunjie Wu, Shu Wang The Journal of Grey System    2021, 33 (2): 1-13.   Abstract （510）            Knowledge map    In the current study, based on grey relational similarity measure and entropy-weight, a comprehensive grey relational similarity measure method for multi-attribute decision making (MADM) problem to evaluate the alternatives has been proposed. A new algorithm based on the same attribute value's comparison and different attribute value's synthesis for the MADM problems is also established. In this algorithm, the ideal attribute values are selected according to attribute properties. Later, the grey relational similarity measure method is used to calculate the grey value between the attribute value and the ideal attribute value in the same attribute. To compare the alternatives, the entropy-weight method is applied to determine the weights for different attributes objectively. Finally, we take the multi-attribute weapon system problem as an example to illustrate the effectiveness and validity of the proposed method. The example verification results show that the method constructed in this paper has higher credibility, and the rank reversal problem has also passed the test. Related Articles | Metrics

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Carbon Emission Prediction Method of Regional Logistics Industry Based on Improved GM(1, N) Model Xueqiang Guo, Bingjun Li The Journal of Grey System    2022, 34 (2): 1-9.   Abstract （423）            Knowledge map    Aiming at the poor prediction performance of the traditional GM(1,N) model, this paper proposes the GM(1,N) model with expression optimization: firstly, unknown parameters are introduced into the coefficient matrix of the traditional GM(1,N) model to obtain the model expression with unknown parameters; Then the average relative error function with unknown parameters is constructed; Finally, the particle swarm optimization algorithm is used to obtain the parameter column with the smallest average relative error. Taking the carbon emission of the logistics industry in Hubei Province as an example, this paper forecasts the carbon emission by using the traditional GM(1,N) model, GM(1, N) model with background value optimization, and GM(1, N) model with expression optimization. By comparing and analyzing the prediction results of the three models, it is concluded that GM(1,N) model with expression optimization has better prediction performance. Related Articles | Metrics

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A Novel Grey Incidence Decision-making Method Embodying Development Tendency and Its Application Heng Ma, Peng Yu, Yingjie Yang, Liangyan Tao, David Mba The Journal of Grey System    2021, 33 (3): 1-15.   Abstract （387）            Knowledge map    In grey incidence decision-making models, the development tendency of each indicator value for the evaluated object is rarely considered, and the degree of discrimination between evaluation values is not high enough sometimes. In view of this, a novel grey incidence decision-making method embodying development tendency is proposed, which can guide the evaluated objects to a better direction in the future and can also distinguish the evaluation results to the greatest extent. Firstly, the development factor is defined, which can exert an effect on the development tendency of each indicator value over time. Secondly, guided by an exponential function, the weighted degree of grey incidence based on exponential function is constructed by combining the maximizing deviation and grey entropy in assigning weights to the indicators. Thirdly, the weights of the time series are delivered by the combined weighting method based on level difference maximization. Hence, the dynamic evaluation values are produced for ranking the evaluated objects. Finally, a practical example of the transformation and upgrading of the manufacturing industry in the Yangtze River Delta (YRD) demonstrates the effectiveness and application of the proposed model. Related Articles | Metrics

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A Framework of Grey Prediction Models on China's Population Aging Under the Perspective of Regional Differences  Weiliang Zhang, Sifeng Liu, Junliang Du, Lianyi Liu, Xiaojun Guo, Zurun Xu The Journal of Grey System    2022, 34 (4): 1-.   Abstract （359）            Knowledge map    Population aging is a major social problem that China is facing. Scientific prediction and correct analysis of population aging are important for resource allocation, policy formulation, and service provision. To this end, this paper proposes a population prediction framework based on grey models to predict and analyze regional differences in China's aging status. Firstly, we construct three indicators, i.e., total population, aged population, and proportion of the aged population, to reflect the aging status of a region. Secondly, we develop a grey model framework to predict and analyze aging differences in the eastern, central, and western regions of China. Finally, according to the prediction and analysis results of the three aging indicators, we suggest some corresponding countermeasures to address the challenges of China's future aging problem. 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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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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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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Modelling Principles of Grey Matrix Incidence Analysis for Panel Data Decai Sun, Dang Luo, Huihui Zhang The Journal of Grey System    2021, 33 (3): 16-30.   Abstract （264）            Knowledge map    Grey incidence analysis (GIA), a branch of grey system theory, is commonly used in a broad range of scientific disciplines, from natural to social sciences. Since most current research on GIA models for panel data focuses on improving them, the mathematical principles and physical interpretations receive relatively limited attention. The principles of grey matrix incidence analysis (GMIA), which allows for both cross-sectional and time-series characteristics of panel data, are proposed in this paper. The panel data is first represented as a matrix, and then the matrix incidence operators are presented, along with theoretical properties and physical interpretations. The modeling principles, including the normativity, closeness, and column permutation independence, are articulated mathematically in a concise manner. The unified representation of GMIA models is then suggested, and the comprehensive procedures for expanding the GIA models for time series into the GMIA models for panel data are illustrated using the generalized GIA model as an example. Finally, the findings of the two examples indicate that the proposed solution has interpretability and robustness advantages over the compared approaches. Related Articles | Metrics

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your manuscript into the box null The Journal of Grey System    Accepted: 21 October 2020

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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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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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A Novel Time-Varying Multivariable Nonlinear Grey Model and Its Application Sandang Guo, Yaqian Jing, Qian Li The Journal of Grey System    2021, 33 (3): 150-163.   Abstract （250）            Knowledge map    This study develops a novel time-varying multivariable nonlinear grey model, namely TVNGM(1,N), which can capture the nonlinear and potential features of dynamic development trends. The novel multivariable nonlinear grey model has introduced a linear time-varying driving coefficient to replace the proposed model's constant parameter and added adjustment coefficient. The new model can be completely compatible with a single variable and multivariable grey models by adjusting different parameter values. For furtherly improving forecasting accuracy, the particle swarm optimization (PSO) algorithm is used to efficiently optimize the model’s parameters. Then, estimated parameters and the connotative prediction formula of the TVNGM(1,N) model are deduced by using the difference equation. To this end, two case studies are selected to prove the practicality of the method and compare it with other models. The results demonstrate that the proposed model has superior performance. Related Articles | Metrics

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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.   Abstract （249）            Knowledge map    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. Related Articles | Metrics

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A Generalized Multivariate Grey Prediction Model DGM(1,N,τi) With Unknown Time Delays Chong Li , Xiuping Xie The Journal of Grey System    2020, 32 (2): 50-76.   Abstract （244）            Knowledge map    Related Articles | Metrics

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Improved Fractional Order Single Optimization Parameter Grey Model Jiangtao Wei, Yonghong Wu The Journal of Grey System    2023, 35 (4): 154-171.   Abstract （244）            Knowledge map    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.  Related Articles | Metrics

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Commonality Refinement and Code Reuse of Grey Prediction Model Based on MATLAB Shuangyi Yang, Bo Zeng, Shuliang Li, Sifeng Liu, Hanif Heidari The Journal of Grey System    2022, 34 (1): 139-153.   Abstract （241）            Knowledge map    This paper realizes the rapid development of the MATLAB of grey prediction models through public module call. Firstly, the multiple modeling steps of grey prediction models are divided into three types: Model, View, and Controller. Then, it is analyzed which steps are completely common to all models. Finally, these steps are encapsulated into general modules similar to JavaBean. These modules can be called program building blocks for compiling grey prediction modeling software, which greatly improves the development efficiency, reduces code redundancy, and improves the stability of the software. This is of great value to the popularization of grey prediction models. Related Articles | Metrics