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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.   Abstract （91）            Knowledge map    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. Related Articles | Metrics

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Multi-steps Carbon Emission Forecasts Using a Novel Grey Multivariable Convolution Model  Song Ding, Juntao Ye, Zhijian Cai, Xing'ao Shen, Huahan Zhang The Journal of Grey System    2024, 36 (3): 11-24.   Abstract （104）            Knowledge map    The accurate forecasting of provincial carbon emissions is pivotal for China as it strives to meet its carbon neutrality goals. To this end, an improved grey multivariable convolution model has been developed, employing a unified new-information-based method for the preliminary accumulation of data. The particle swarm optimization (PSO) algorithm is then applied to determine the optimal parameters within this sophisticated model. Moreover, to identify the relevant factors for provincial carbon emissions, a comprehensive determination of these factors was conducted from two aspects: literature research and grey relational analysis. For validation, carbon emission data from two provinces are analyzed, and the model’s efficacy is thoroughly compared with five competitors across three different predictive horizons. The empirical results indicate that the proposed model has distinct advantages over the competing models. Additionally, the model’s robustness and comprehensive forecasting abilities for provincial carbon emissions are confirmed through detailed Monte Carlo simulations and parameter sensitivity analyses across various forecasting horizons.   Related Articles | Metrics

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Grey Generalized Stochastic Petri-Bayesian Network Testability Model for High-reliability Complex Systems  Cuiping Niu, Zhigeng Fang, Shuyu Xiao, Youpeng Liu The Journal of Grey System    2024, 36 (3): 37-50.   Abstract （117）            Knowledge map    Aiming at the issues of paucity of fault information, complexity of functional logic relationships between fault modes, and uncertainty of fault information and its propagation path in the testability analysis of high-reliability complex systems, a grey generalized stochastic Petri-Bayesian network (Grey-GSPBN) testability model is proposed in this study. Firstly, typical failure modes and their severity are obtained through the failure modes, effects and analysis (FMECA) study, and the failure modes are coded and coloured accordingly to construct the generalized stochastic Petri network (GSPN) model. Then, the correlation matrix between failure modes and test points is established by using the reachability algorithm, based on which the equivalent isomorphic grey Bayesian network (GBN) model is established, and grey number theory is introduced to integrate multi-source grey information to determine the grey prior and posterior distribution matrix of testability indexes. Finally, the grey probabilistic testability evaluation matrix is calculated using GreyGSPBN model, and the testability indicators are analyzed. A certain liquid rocket engine system is taken as a case to verify the scientificity and superiority of the proposed model in the testability modelling of high-reliability complex systems, and the model can provide a valuable reference for engineering applications Related Articles | Metrics

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Predicting Solar Array Power Output on a Spacecraft Using a Fractional-Order Grey Model and Particle Swarm Optimization  Liang Ren, Yuanhe Gao, Feng Yang, Yongcong He The Journal of Grey System    2024, 36 (3): 86-97.   Abstract （63）            Knowledge map    During eclipse periods, the spacecraft relies on electricity, which its solar arrays produce and store in batteries. Forecasting a solar array’s power output employed during space missions is of significant importance. Varying space environments and satellite loads, which are characterized by significant randomness and uncertainty, affect the generated power of the spacecraft’s solar array. These challenges pose difficulties in power prediction. To address these issues and achieve a more accurate estimation of the solar array’s generated power during a space mission, this study develops a metabolic model termed TDGM(1, 1, r) that incorporates an enhanced accumulating fractional-order, optimizing it within the discrete grey TDGM(1,1) model’s framework with three parameters. The optimization model’s objective function is defined as the mean absolute percentage error (MAPE) within the modeling context. In order to minimize MAPE, the differential equation’s order and accumulation number are determined using a particle swarm approach. The TDGM(1, 1, r) demonstrates superior forecasting performance in comparison to the classical GM(1,1) and Grey–Markov models. These findings indi-cate the superiority of TDGM(1,1,r) over GM(1,1) and Grey–Markov, with improvements of 84.2% and 81.2% for MAPE (from 1.83% to 0.29% and from 1.54% to 0.29%). The metabolic TDGM(1,1,r) employing the particle swarm algorithm (PSO) is better suited for short-term predictions. Finally, relevant suggestions for future development of the prediction model are proposed.   Related Articles | Metrics

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Exploring Death Population Prediction and Cemetery Planning in Chongqing amid an Aging Population: A Grey Forecast Model Based on Interval Grey Number  Huaan Wu, Yuhua Jin, Yinhe Xue, Bo Zeng, Hui Wang The Journal of Grey System    2024, 36 (3): 51-62.   Abstract （195）            Knowledge map    China’s population is steadily aging, contributing to the increase in the number of deceased people and the growing disparity between supply and demand for cemeteries. To provide theoretical support and data reference for cemetery planning, this study considers Chongqing, a city with a high rate of aging population, as an example to apply the interval grey number model to model and predict the size of the death population in Chongqing. The following conclusions are drawn: (1) The accuracy of the interval grey number prediction model in simulating the size of the death population in Chongqing exceeds 98%, indicating that the model employed in the study is suitable for medium- to long-term prediction; (2) The prediction results show that the annual death scale of registered population in Chongqing will range between 220 and 330 thousand from 2022 to 2030, with a fluctuating upward trend; (3) According to the size of the death population predicted, the cemetery market in Chongqing will experience a shortage of supply within 10 years. Therefore, in order to ensure a balance between the supply and demand of cemeteries in Chongqing, the government should actively promote the concept of green funerals and reduce the demand for cemeteries. Alternatively, it is also necessary to accelerate the planning and construction of cemeteries to avoid the predicament of people wanting to be buried without a tomb.   Related Articles | Metrics

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A New Optimized Grey Forecasting Model with Polynomial Term and Its Application An Wang, Yaoguo Dang, Junjie Wang The Journal of Grey System    2024, 36 (3): 74-85.   Abstract （219）            Knowledge map    China’s total energy consumption and production rank first in the world. However, China’s energy structure is not reasonable. Therefore, accurate prediction of future energy trends is of great significance for the Chinese government to adjust the energy structure. In this paper, we propose an optimized Grey Euler model with polynomial term, which is abbreviated as OSGEM(1,1,N), to forecast the total energy consumption and production of China in comparison with the commonly used prediction models. The data from 2002 to 2018 are used to simulate the parameters in the proposed model, and the data from 2019 to 2021 are used to test the improved approach. The results show that the OSGEM(1,1,N) model outperforms the other models. Finally, the OSGEM(1,1,N) model is used to forecast the total energy consumption of China from 2022 to 2025 and different results from the previous research results have been obtained.   Related Articles | Metrics

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Ordinal Multivariate Grey Incidence Model and Its Application on Early Warning of Construction Quality Risk  Ke Zhang, Min Ma, Feizhen Zhang, Yuxin Zhou, Chunyong She, Zheng Zhang The Journal of Grey System    2024, 36 (3): 1-10.   Abstract （134）            Knowledge map    Government supervision is the highest level of construction quality management system. Due to a large number of constructions in progress, timely and accurate risk early warning is imperative for improving the efficiency of supervision. Aiming at the small-scale, ordinal, and unequal length multivariate time series of government supervision data, this paper proposes a construction quality risk early warning method based on ordinal multivariate grey incidence analysis. Firstly, to measure the dynamic similarity between risk indicators of projects, the proximity grey incidence model based on ordinal dynamic time warping (DTW) and the similarity grey incidence model based on ordinal L1 norm DTW are constructed respectively. Then, the two models are integrated to construct a comprehensive similarity model for construction quality risk warning. Combining the comprehensive similarity and k-nearest neighbour (k-NN) algorithm, a method of construction quality risk level classification and early warning is constructed. Finally, the method is applied to the quality supervision of water conservancy and hydropower projects in Zhejiang Province, and the results show that the proposed method can effectively solve the problem of construction quality risk early warning based on small-scale and ordinal data. Related Articles | Metrics

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Some Properties of Generalized Whiteness of Interval Grey Number Li Li, Xican Li The Journal of Grey System    2024, 36 (3): 25-36.   Abstract （154）            Knowledge map    In order to mine the intrinsic information of interval grey number, the concept of the generalized whiteness of interval grey number is first given in this paper based on the generalized greyness of interval grey number. Then the static and dynamic properties of generalized whiteness on bounded background domain, infinite background domain and infinitesimal background domain are analyzed, and the concepts of the extreme white system and extreme white spot are given. Finally, the conservation law of the generalized whiteness of interval grey numbers is given, and the generalized whiteness is applied to the ranking of interval grey numbers. The results show that the generalized whiteness of interval grey number on the bounded background domain has the static properties of the relativity, normality, unity, opposition, connectivity, justice and graduality; while on the infinite background domain and the infinitesimal background domain, the generalized whiteness of interval grey number has the above static properties except the graduality. On the bounded background domain, the generalized whiteness changes with the expansion of the background domain and the value domain, while on the infinite background domain and the infinitesimal background domain, the static and dynamic properties of the generalized whiteness of interval grey number are the same, it is not affected by the expansion change of the background domain and value domain, and the generalized whiteness of interval grey numbers is conserved. The research results not only enrich the grey system theory, but also provide a theoretical basis for the analysis and utilization of interval grey numbers. Related Articles | Metrics

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Research on China's GDP Growth Forecast Based on Grey Machine Learning Model Tianxiang Yao, Xichun Liu The Journal of Grey System    2024, 36 (4): 1-13.   Abstract （195）            Knowledge map    Based on Keynesian macroeconomic theory, this paper introduces economic indicators with Chinese characteristics, and constructs a multivariate grey machine learning forecasting model (IGM (1, N, X1 (0) )-IPSO-LSTM) to predict China's GDP growth. Firstly, IGM (1, N) model is constructed by changing the background value construction method of GM (1, N) model and introducing grey action constant A which reflects the change from the grey differential equation to the difference equation. Secondly, due to the low frequency and small amount of GDP data, constructing a two-layer LSTM model to increase the model complexity, so that the data can be fully trained. In addition, this paper uses nonlinear descending function instead of w to construct Improved Particle Swarm Optimization algorithm (IPSO), and adds Genetic Algorithm (GA) to IPSO to reduce the risk of particles falling into the local optimal solution. Finally, using IPSO to find the optimal parameters of LSTM model to predict China's GDP growth. By comparing the prediction accuracy of IGM (1, N, X1 (0) )-IPSO-LSTM model with other benchmark models, the prediction result of IGM (1, N, X1 (0) )-IPSO-LSTM model is the best. It is predicted that China's GDP growth rate in 2024 is 5.18% and in 2025 is 5.12%. By analyzing the trend development of China's economic, it is found that the forecast results are consistent with the expected trend of macro economy, which increases the credibility of the forecast results.   Related Articles | Metrics

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Maintenance Modeling and Grey Lease Pricing for a Series Manufacturing System with the Machines from Multiple Suppliers Yaping Li, Yuhong Cheng, Tangbin Xia, Zhen Chen, Naiming Xie, Ershun Pan The Journal of Grey System    2024, 36 (4): 14-25.   Abstract （94）            Knowledge map    Leasing is an important mode of service-oriented manufacturing where a manufacturer may lease machines from multiple suppliers to form a manufacturing system. While the suppliers provide machine maintenance, their individual interests may not be necessarily optimal to the system. Therefore, we propose a maintenance modeling and lease pricing (MMLP) framework to find the optimal maintenance policy for the system, and make a lease pricing scheme as an incentive mechanism to promote the realization of the cooperative maintenance among the suppliers. An optimization model is established to obtain a long-term maintenance policy by minimizing a cost rate function. And then, the grey lease pricing scheme based on the fair allocation of the benefits from the cooperation is suggested, with the marginal contribution of each supplier in the cooperation measured by the grey Shapley value method. Finally, a case study is used to show the application of the MMLP framework, presenting that the joining of the suppliers can make maintenance cost reduced and that the lease prices determined by using the grey Shapley value demonstrate the emergence and risk of the cooperation. Related Articles | Metrics

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Hydrogen Load Demand Prediction in Unified Energy System Based on Grey Ridgelet Neural Network Dou Qin, Bin Zhao The Journal of Grey System    2024, 36 (4): 26-32.   Abstract （109）            Knowledge map    Hydrogen will play critical pole in industrial field, heating field and transportation field, which can achieve mutual conversion of different energies. Hydrogen load prediction demand is important for establishing unified energy system, a novel prediction model is established based on particle swarm algorithm (PSA) and grey Ridgelet neural network (GRNN) to improve medium and long term hydrogen load demand prediction accuracy. Firstly hydrogen load demand prediction model in unified energy system is established, which concludes hydrogen load demand prediction models in industrial field, heating field and transportation field, and then total hydrogen demand model is deduced. Secondly, model of GRNN is constructed based on grey system theory and Ridgelet neural network, analysis procedure of GRNN is established. Structure of GRNN is confirmed, and mathematical model is constructed. To enhance prediction effectiveness of GRNN, PSA is used to optimize parameters of GRNN. Finally hydrogen load demand data in a province is selected to carry out prediction simulation, results show that prediction error of proposed PSA-GRNN ranges from 1.88% to 3.02%, which is less than that of other three prediction models, and fit goodness of proposed PSA-GRNN ranges from 0.958 to 0.985, which is also less than that of other three prediction models. Therefore proposed PSA-GRNN has better prediction precision and efficiency, which can obtain better precision effect and applicability. Hydrogen load demand prediction results in heating field based on PSAGRNN are closer to real value than that based on other three prediction models, results show that proposed PSA-GRNN has better prediction accuracy that other three prediction models.   Related Articles | Metrics

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Construction of Symbiosis System for Rural Industry Revitalization Based on Lotka-Volterra Model and Stability Strategy Study  Na Zhang, Shuting Shi, Zihao Li The Journal of Grey System    2024, 36 (4): 33-54.   Abstract （123）            Knowledge map    The symbiotic system of rural industrial revitalization comprises farming households, grassroots governments, and new rural collective economies as symbiotic units. The optimal symbiosis mode within this symbiotic system is reciprocal symbiosis. This study focuses on Yuhang District in Zhejiang Province, Yining County in Xinjiang Uygur Autonomous Region, and Wangcheng District in Hunan Province as research areas. Firstly, the grey Lotka-Volterra (GLV) model is employed to analyze the interaction within the current symbiotic system of rural industrial revitalization across these regions using data from 2019-2023. Secondly, this paper utilizes the GM(1,1) model to predict future data for these regions and analyze their future symbiosis. Subsequently, this paper examines the equilibrium point and stability of the symbiosis systems within these regions. Finally, based on an evolutionary game model approach, key factors influencing the evolution of a stable symbiosis system when satisfying and balancing interest demands among symbiotic units are explored. The findings reveal distinct characteristics within each subject's rural industrial revitalization symbiotic system. Government subsidies' intensity and cooperation benefits and costs primarily influence its evolution towards stability.  Related Articles | Metrics

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Grey Information Relational Estimation Model of Soil Organic Matter Content Based on Hyperspectral data Hong Che, Xican Li, Guozhi Xu The Journal of Grey System    2024, 36 (4): 56-68.   Abstract （171）            Knowledge map    In order to overcome the uncertainty in hyperspectral estimation of soil organic matter content, this paper aim to establish a grey information relational estimation model of soil organic matter content based on hyperspectral data and grey information theory. Based on 76 samples in Zhangqiu District of Jinan City, Shandong province of China, the spectral data are first transformed by the nine methods such as square root, first order differentiation of the logarithm reciprocal, and so on, the correlation coefficient is calculated, and the estimation factors are selected by using the principle of great maximum correlation. Then, according to the principle of increasing information and taking maximum method, the spectral estimation factors of each sample are sorted from small to large, and the grey information sequence is formed, and the grey relational estimation model of soil organic matter content is constructed based on the information chain. Finally, the estimation results based on different information chains are fused twice, and compared with the commonly used estimation methods. The results of the method in this paper show that the average relative error of the 12 test samples is 5.576%, and the determination coefficient R2 is 0.934, and the estimation accuracy is higher than that of commonly used methods such as multiple linear regression, BP neural network and support vector machine. The results show that the grey information relational estimation model using hyperspectral data proposed in this paper is feasible and effective, and it provides a new way for hyperspectral estimation of soil organic matter and other soil properties.   Related Articles | Metrics

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Prediction of Digital Economy Development Levels in Urban Cities Based on the GCSA-GM(1,N) Model Chengxuan Wu, Cheng Tian, Fang Wang, Wenxin Cheng The Journal of Grey System    2024, 36 (4): 69-77.   Abstract （139）            Knowledge map    Based on the digital economy index (DEI) and Technological Innovation, Industrial Structure, GDP and Openness to the Development Index data of 15 sub-provincial cities from 2017 to 2021, we construct a framework to predict the development potential of the urban digital economy and analyse the spatial evolution trend under the ‘small data’ scenario using geometric causal strength analysis GM(1,N) and the gravity center model. The empirical analysis reveals that,15 sub-provincial cities, at least one of the influencing factors has a causal relationship with the urban DEI that is greater than 0.5. The average forecast error of the GM(1,N) model based on causality strength in 15 sub-provincial cities is less than 1% in 2022. This reflects that four influencing factors can be used as an effective indicator to measure the level of digital economic development. The forecast results also indicate that the digital economy center of China’s sub-provincial cities will evolve from north to south and from east to west in 2022-2025. Finally, this study presents suggestions from three aspects: Strengthening technological innovation, promoting industrial digital transformation and upgrading, and strengthening cross-regional cooperation and exchanges.   Related Articles | Metrics

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Residual Life Prediction of High-pressure Pipeline Erosion Based on the Grey Markov Model Liu Xiong, Mo Li The Journal of Grey System    2024, 36 (4): 78-89.   Abstract （69）            Knowledge map    Based on the digital economy index (DEI) and Technological Innovation, Industrial Structure, GDP and Openness to the Development Index data of 15 sub-provincial cities from 2017 to 2021, we construct a framework to predict the development potential of the urban digital economy and analyse the spatial evolution trend under the ‘small data’ scenario using geometric causal strength analysis GM(1,N) and the gravity center model. The empirical analysis reveals that,15 sub-provincial cities, at least one of the influencing factors has a causal relationship with the urban DEI that is greater than 0.5. The average forecast error of the GM(1,N) model based on causality strength in 15 sub-provincial cities is less than 1% in 2022. This reflects that four influencing factors can be used as an effective indicator to measure the level of digital economic development. The forecast results also indicate that the digital economy center of China’s sub-provincial cities will evolve from north to south and from east to west in 2022-2025. Finally, this study presents suggestions from three aspects: Strengthening technological innovation, promoting industrial digital transformation and upgrading, and strengthening cross-regional cooperation and exchanges.   Related Articles | Metrics

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Assessing the Service Quality of Fisherman's Homestays in China: a Hybrid MADM Approach Consisting of DANP and Grey Clustering Evaluation Peng Jiang, Rui Chi, Hui Xia, Longyun Zhang, Chuandong Ju The Journal of Grey System    2024, 36 (4): 90-110.   Abstract （100）            Knowledge map    Nowadays, a new emerging tourism industry, named fisherman's homestay, has become a very representative marine leisure tourism project, widely promoted in coastal areas in China. However, the development of China's fisherman's homestay industry is not yet mature and there are many problems, such as incomplete laws and regulations, lack of infrastructure, and severe homogenization. Therefore, it is very important to help the owners of fisherman's homestay improve the service quality. Based on the Service Quality Gap Model, this paper establishes an evaluation index that affects the service quality of fishermen's homestay. We apply decisionmaking trial and evaluation laboratory-based analytic network process (DANP) to identify the critical factors and the causal relationship between them. And the grey clustering model is used to evaluate the service quality of Liaoning province and other five places. Experimental results reveal those six factors, including surrounding facilities, online marketing, room infrastructure, personalized service, community co-prosperity, and attention to harmonization with the environment, contribute to improving the service quality of fisherman's homestays. The fisherman's homestays in Shandong Province, Liaoning Province, and Zhejiang Province are in "excellent" level, and the fisherman's homestays in Fujian Province and Guangxi Zhuang Autonomous Region are in "good" level.  Related Articles | Metrics

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Evaluation of Barriers to Disabled Elderly’s Access to eHealth in China Using Grey Relational Analysis Muhammad Nawaz, Sifeng Liu, Naiming Xie, Mohammed Atef, Muhammad Wasif Hanif The Journal of Grey System    2024, 36 (5): 1-14.   Abstract （151）            Knowledge map    This study aimed to identify and rank the barriers faced by disabled elderly in China while accessing eHealth primary care services. Primary data were collected from the disabled elderly based on technological, individual, relational, environmental, and organizational constructs. The Dynamic Grey Relational Analysis (DGRA) and Multiple-criteria Decision-making (MCDM) based TOPSIS techniques were used to identify and rank the barriers. We found that the most significant barrier was “aging limitation (reduction in hearing, sight, memory, and fine motor control)” in both (DGRA and MCDM) cases. The Kruskal-Wallis test was used to investigate the significance of this barrier in different age groups of disabled elderly. We found no significant differences among the three age groups of disabled elderly, which shows that the barrier “aging limitation (reduction in hearing, sight, memory, and fine motor control)” is the most significant barrier at each age group (when age ≥ 60) of disabled elderly. The average value of Grey Relational Grades (GRGaverage) and the sorting outcomes of the MCDM of the construct individual were higher than those of all other constructs. This study is the first of its kind to apply the DGRA, MCDM and KWT to expose the barriers while accessing eHealth services for the disabled elderly in China.   Related Articles | Metrics

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Entropy-weighted TOPSIS Multi-attribute Decision-making Model and Its Applications Based on Generalized Greyness Li Zhang, Xican Li The Journal of Grey System    2024, 36 (5): 15-26.   Abstract （245）            Knowledge map    In order to solve the decision-making problem that the attributive values are internal grey numbers and the attributive weights are unknown, this paper try to construct an entropy-weighted TOPSIS model based on the generalized greyness of interval grey number from the perspectives of proximity and equilibrium. Firstly, the properties of greyness distance are analyzed and the simplified formula for computing greyness distance is given. Then, a method to determine entropy weight based on greyness distance is given, and an entropy weighted TOPSIS decision-making model is established. Finally, the constructed model is applied to selecting brackish water irrigation pattern of winter wheat in North China Plain, China, so to verify its feasibility and effectiveness. The results show that the model proposed in this paper not only fully utilizes the measurement information of interval grey numbers, but also overcomes the influence of subjective factors on weights, and provide a new method for decision-making of unknown attributive weights and attributive value with interval grey number, and the interval grey numbers coexist with the real numbers. The application examples show that the model proposed in this paper is feasible and valid.  Related Articles | Metrics

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Seasonal Grey Forecasting Model Based on Damping Accumulation and Its Application Ye Li, Chengyun Wang, Qiwen Wei, Shi Yao The Journal of Grey System    2024, 36 (5): 27-42.   Abstract （119）            Knowledge map    A new damping nonlinear grey multivariate seasonal forecasting power model DAFGM(1,N, , ) is proposed to solve the problem of small sample forecasting with seasonal, nonlinear, and uncertain system behavior characteristic sequence. Firstly, the seasonal moving filter is used to eliminate the seasonal characteristics of the original series. Then, according to the principle of "new information priority ", the damping accumulation coefficient is introduced, the unknown factors which are difficult to collect are simulated by introducing dummy variables, and a new seasonal forecasting model is constructed. Finally, the model is used to forecast the quarterly wind power generation in China. The results show that the model has good practicability and effectiveness.   Related Articles | Metrics

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Novel Grey SIRS Model Forecasts Credit Risk with Nonlinear Infection Qian Lv, Xinping Xiao, Mingyun Gao The Journal of Grey System    2024, 36 (5): 43-57.   Abstract （66）            Knowledge map    Epidemic models are widely used in financial risk prediction. The problems of nonlinear changes in infection rates and limited data samples in financial risk remain to be addressed. To this end, this paper proposes a nonlinear grey SIRS (abbreviated as GSIRS) model based on short-term data. This model employs a time-varying function to capture the nonlinear dynamics of infection rates, and integrates the system grey prediction model to analyze short-term data. Parameter optimization is achieved through the least square method and the whale optimization algorithm. The GSIRS model shows good prediction accuracy across three financial crisis datasets, with MAPE ranging from 3.379% to 4.981% for training sets and 2.913% to 3.212% for test sets. These values are significantly better than those of competition models. In addition, the CWC values of the interval prediction under the 95% confidence level of the model are 0.13, 0.14 and 0.33, respectively. The combination of excellent RMSE and STD metrics further proves the stable forecasting ability. Meanwhile, the sensitivity analysis shows that changes of infection rate have a 1-2 period lagged effect on the infected individual density.   Related Articles | Metrics