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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.  
    Abstract259)           
    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. 
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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.  
    Abstract234)           
    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.  
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    The Greyness and Applications of Grey Set
    Xican Li, Li Li
    The Journal of Grey System    2024, 36 (6): 42-53.  
    Abstract224)           
    In order to quantitatively describe the grey properties of grey set, based on the possibility function of grey set, this paper discusses the expression method of the greyness of grey set and its applications. Firstly, the axiomatic definition and a method of calculating the greyness of grey set are given, and its rationality is analyzed through examples. Then, according to the principle of unity of opposites, the concept of whiteness of grey set is given, and the applications of greyness of grey set are analyzed. Finally, some examples are given to verify the validity of greyness of grey set and its application model. The results show that the axiomatic definition of greyness of grey set not only conforms to the grey immortal axiom, but also can quantitatively describes the dynamic evolution state of grey hazy set (grey set). The application examples show that the grey relational degree model and the grey decision model based on the greyness of grey set are feasible and effective. The research results not only enrich the theory of grey mathematics and grey system, but also provide a new method for grey relational analysis and grey decision.  
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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.  
    Abstract215)           
    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.  
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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.  
    Abstract203)           
    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.  
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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.  
    Abstract190)           
    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.  
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    Forecasting the Two-Stage Regional Population Ageing Structure by Employing Grey Compositional Model 
    Hui Li, Naiming Xie, Rafał Mierzwiak
    The Journal of Grey System    2025, 37 (1): 1-15.  
    Abstract183)           
    Population ageing is a significant and global concern, particularly pronounced in China, where rapid ageing growth has been observed. This growth is uneven across regions, presenting urgent challenges for local governments. Accurate forecast of regional ageing structure is vital for developing and adjusting population, social, and economic policies. To address this, based on the compositional data, population ageing is firstly delineated into two stages: the structure of the elderly and that of the disabled elderly, and a data collection and pre-processing framework based on this division is constructed. Then, a novel non-linear dynamic grey Markov compositional model is developed to tackle this two-stage issue. Finally, using this model, the ageing structure is predicted and studied in Jiangsu Province, China, as an illustrative case. Experimental results show that the ageing structure will be further “aged” and “disabled”, and moderate disability is the core component of the rise in the disabled elderly. These forecasts align with current trends in ageing and provide a quantitative basis for governmental policy-making and adjustments.  
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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.  
    Abstract173)           
    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.
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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.  
    Abstract158)           
    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.  
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    Data-driven Dynamic Grey-Verhulst SEIRD Model for Public Health Emergencies Forecasting
    Shuhua Zhang, Ming Liu, Bingjun Li
    The Journal of Grey System    2025, 37 (1): 33-46.  
    Abstract154)           
    Determining parameters in infectious disease dynamics models is crucial for simulating and predicting the development trends of public health emergencies. Utilizing real-time epidemic data and grey systems theory, our innovative approach bridges the Dynamic Grey Verhulst model and the SEIRD model, which respectively have advantages in short-term and long-term forecasting. The new model features a dynamically adjusting decision cycle to accommodate evolving epidemic data. We constructed a dynamic grey Verhulst model using the principle of metabolism, enabling it to dynamically update and iterate important parameters of infectious disease models. This results in accurate simulation and prediction of epidemic dynamics. Taking the SARS-CoV-2 Omicron outbreak in Shanghai, China, in the spring of 2022 as an example, the proposed Dynamic Grey-Verhulst SEIRD model (DGVM-SEIRD) provides a data-driven, high-sensitivity and high-precision method for predicting public health emergencies. Sensitivity tests also confirm the superiority of our model. Furthermore, validation with H1N1 influenza data from Beijing, the COVID-19 outbreak in Wuhan and SARSCoV-2 emergencies in the UK reinforces our model’s accuracy. This methodology provides a highly flexible and responsive analytical tool for public health emergency management, offering scientific support for formulating more effective epidemic prevention and control strategies and emergency responses. 
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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.  
    Abstract153)           
    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.  
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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.  
    Abstract151)           
    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.
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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.  
    Abstract138)           
    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. 
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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.  
    Abstract132)           
    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.  
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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.  
    Abstract130)           
    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
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    Research on Grey Prediction of Regional Dual Energy Consumption Under Carbon Emission Constraints
    Yuhan Xie, Chuanmin Mi
    The Journal of Grey System    2025, 37 (1): 79-95.  
    Abstract123)           
    To enhance the modeling capability of the grey prediction model in the spatiotemporal domain, the paper proposes a novel spatiotemporal grey prediction model integrated with heterogeneous adjacency accumulation. Initially, an improved economic geographic gravity matrix is employed to characterize the spatial flow patterns of regional energy consumption, vividly illustrating the spatial interplay between non-adjacent provinces. Subsequently, a heterogeneous adjacent accumulation operator is incorporated to mirror regional discrepancies in energy consumption and bolster the robustness of the spatiotemporal prediction model. Ultimately, the novel prediction model is utilized to forecast the evolution of regional dual energy consumption within the constraints of carbon emissions. The findings of this research reveal the following: (1) By 2030, the total energy demand is projected to surge to 6.839 billion tons of standard coal, surpassing the predefined threshold of 6 billion tons. The prompt implementation of energy-saving strategies is paramount to expedite the attainment of carbon peaking. (2) Energy consumption intensity exhibits notable regional variability, with a spatially positive correlation in energy consumption intensity among regions. By 2030, it is anticipated that only 12 provinces, including Beijing, Guangdong, Shanghai, and Jiangsu, will attain the energy efficiency benchmarks of advanced developed countries.
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    Comparative Analysis of Grey Forecasting Models for Population Aging Prediction: A Case Study of Egypt's Demographic Evolution
    Islam Mahmoud Sharafeldin, Naiming Xie
    The Journal of Grey System    2025, 37 (1): 108-117.  
    Abstract121)           
    Population aging in developing nations presents complex demographic challenges that conventional forecasting approaches often struggle to address effectively, particularly when confronted with endogenous volatility in demographic structures and limited data availability. This study introduces an enhanced hybrid grey forecasting framework to predict population aging patterns in Egypt, incorporating advanced grey models to improve prediction accuracy and capture regional demographic variations. Using comprehensive demographic data from 2011-2023, we evaluate multiple grey forecasting models to identify optimal prediction methodologies for different population segments. Our findings reveal that the Grey Optimization Model with Interval Analysis (GOM_IA (1,1)) demonstrates superior predictive performance, achieving the lowest Mean Absolute Percentage Error for urban populations, rural and aged populations during the testing period. While, Unbiased GOM (1,1) model give the best performance for the total population prediction over the other grey models. The model projects significant regional variations in aging patterns, with urban areas experiencing accelerated aging rates compared to rural regions. This study makes several key contributions by it establishing a robust methodological framework for demographic forecasting in developing nations with limited data availability. As well as providing quantitative evidence of regional disparities in aging patterns across Egypt. Finally, offering a data-driven insights for policy formulation in healthcare infrastructure development and social service delivery. The findings have significant implications for resource allocation and policy planning in Egypt and other developing nations experiencing similar demographic transitions. Furthermore, our research demonstrated the effectiveness of grey forecasting models in capturing complex demographic patterns and supports evidence-based decision-making in addressing the challenges of population aging.
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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.  
    Abstract121)           
    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.  
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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.  
    Abstract116)           
    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. 
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    A Novel Power-sum Time-varying Grey Prediction Model and Its Applications
    Kai Cai, Lianyi Liu, Sifeng Liu
    The Journal of Grey System    2025, 37 (1): 64-78.  
    Abstract116)           
    The purpose of this paper is to propose an improved power-sum accumulation time-varying grey model (PATGM) to enhance the ability to mine the heterogeneity of sparse data. Firstly, a novel power-sum accumulation grey generating operator is introduced to smooth the observed values according to data fluctuations, mitigating the model's ill-conditioned property. Secondly, a time-varying function is introduced as a parameter structure to the traditional model, providing the model with flexibility in complex systems modeling. Finally, based on the Dingo Optimization Algorithm, a hyperparameter calibration strategy for PATGM is provided. The power-sum accumulation grey generating operator can amplify or minimize the nonlinear characteristics of the observations, thus significantly improving the adaptivity of the grey modeling approach to fluctuating sequences. Meanwhile, the elastic-net regression method is employed to obtain a more reasonable and stable parameter structure. The hyperparameters are calculated using the Dingo optimization algorithm, which effectively controls the noise resistance and nonlinearity in the prediction system. PATGM solves the data smoothing processing and model structure selection problems of the traditional grey model. This new model is suitable for processing data prediction tasks with complex characteristics, especially provides an effective prediction method for complex engineering and system modeling. 
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