The Journal of Grey System

An Extended Conformable Fractional Stochastic Grey Model and its Analysis in System Prediction#br#

Yang Yang, Di Zhang, Xiuqin Wang

2025, 37(6): 1-13.

Asbtract ( 21 )

Related Articles | Metrics

Grey models are widely researched for system modelling and analysis. Considering the complexity of practical problems, grey models with both fractional and stochastic calculus can be used for mining the changing trend of the system with certain interference and uncertainty. For the simple expression and easier calculation of conformable fractional calculus, the conformable fractional stochastic grey model is proposed and discussed. The proposed model includes both random and deterministic factors, which can utilize the excellent characteristics of fractional and stochastic grey models. Several examples are used to test the performance of the proposed model. As a broader category model, conformable fractional stochastic grey one can integrate and expand the existing model with better physical meaning. The results show that new model has good performances in model analysis and short-term prediction. More novel models and application could be achieved for data mining, complex physical problems modelling and prediction.

A Novel Seasonal Grey Model with Time Power Terms for High-accuracy Quarterly Electricity Consumption Forecasting

Xuexiu Fan, Keshen Jiang, Zedong Xu

2025, 37(6): 14-27.

Asbtract ( 8 )

Related Articles | Metrics

Quarterly electricity consumption forecasting poses significant challenges due to its inherent characteristics of periodic oscillations, nonlinear fluctuations, and temporal trends, driven by seasonal variations and macroeconomic dynamics. This study proposes a seasonal grey model with time power terms (abbreviated as SPGM(1,1)) that integrates trigonometric seasonality components and time-variant power terms into the grey system framework. We rigorously derive the model’s discrete formulation and time response sequence. To enhance the model’s efficacy, a particle swarm optimization (PSO) algorithm is adopted to calibrate the model’s nonlinear parameters. To demonstrate the effectiveness and superiority of the SPGM(1,1) model, this model is applied to simulate and predict Guangzhou’s quarterly electricity consumption data (2018Q1-2023Q4). The numerical results show that the proposed model demonstrates a better performance than the other grey models, the statistical econometric model and the machine learning model. Furthermore, to validate the robustness and stability of the new model, we trained it using datasets with varying proportions. The results demonstrate that the SPGM (1,1) model can adaptively fit and predict data sequences. Therefore, the SPGM(1,1) model is utilized to predict Guangzhou’s quarterly electricity consumption by 2025, inferring that electricity consumption will continue to exhibit a growth tendency with seasonal fluctuations. Based on the attained forecasts, several suggestions are put forward to promote the sustainable development of Guangzhou’s electricity consumption, supporting the evaluation of China’s power system reform pilot programs to derive actionable insights for optimizing energy systems in similar cities globally.

Prioritizing Barriers and Potential Solutions for Solar Energy Development in China: A dynamic Grey Relational Analysis and TOPSIS Approach#br#

Ismail Kamdar, Sifeng Liu, Weiliang Zhang

2025, 37(6): 28-39.

Asbtract ( 11 )

Related Articles | Metrics

Among various renewable energy sources, solar energy is particularly attractive due to its abundance in China. However, several barriers hinder the development of solar energy in the country. This study followed a systematic approach to identify country-specific barriers and corresponding solutions. A total of 17 barriers were identified and categorized into six groups: technical, economic, social, political, institutional, and environmental. To overcome these barriers, six potential solutions were proposed. The dynamic grey relational analysis (dynamic GRA) approach was then applied to evaluate and prioritize these barriers, and the technique for order of preference by similarity to ideal solution (TOPSIS) approach was used to assess the potential solutions. The dynamic GRA approach revealed that “high initial capital costs” and “energy storage challenges” in the economic and technical groups are the most significant barriers to
solar energy development in China. Meanwhile, the TOPSIS approach indicated that “financial and economic incentives” and “regulatory and policy reforms” are the most effective solutions to these barriers. This study is the first to incorporate environmental factors and apply the dynamic GRA to evaluate barriers to solar energy development. The findings provide important insights and practical recommendations for energy professionals and policymakers.

Corrosion Rate Prediction of Oil and Gas Pipelines Based on VMD-KPCA-Optimized GM (1, N) Power Model#br#

Donghai Yang, Mingzhang Zhuang, Jiaxu Miao

2025, 37(6): 40-52.

Asbtract ( 11 )

Related Articles | Metrics

At present, the data regarding oil and gas pipeline corrosion rate prediction collected in oilfields is characterized by a limited number of samples, a limited variety of types, and the absence of linear regularity. In light of these characteristics, this paper intends to adopt an improved approach for accurately predicting the corrosion rate of oil and gas pipelines. Firstly, variational mode decomposition (VMD) is utilized to decompose various pipeline corrosion factors. This method decomposes the limited pipeline corrosion factors into new variables with distinct features, thereby making effective use of the collected data. Subsequently, kernel principal component analysis (KPCA) is employed to reduce the dimensionality of the decomposed new variables of the corrosion factors, a minimizing data
redundancy. Finally, the GM (1, N) power model with structural enhancements and optimized background - value calculation is used for modeling and prediction. The prediction results of the VMD - KPCA - OGM (1, N) are compared with those of the GRA - OGM (1, N), VMD - OGM (1, N), and GRA - OGM (1, N) - GABP. The results show that VMD addresses the end effect and mode mixing issues of the EMD during the decomposition of pipeline corrosion rate prediction data, enabling more effective extraction of each principal component. Simultaneously, compared to the PCA, the KPCA exhibits a more pronounced dimension - reduction effect on nonlinear data. The prediction model established by integrating these three methods demonstrates a higher training fitting degree and prediction
accuracy for the corrosion rate prediction data than other models. Its Mean Absolute Percentage Error (MAPE) is 1.4856%, the lowest among the four models. Consequently, this model proves to be an effective means of reflecting the variations in the corrosion rate of pipelines.

A Time Delayed Discrete Grey Power Model with Dynamic Background Value and Its Application in Forecasting Master's Enrollment Scale#br#

Xin Lu, Yongwei Cheng, Ying Wang, Wei Meng

2025, 37(6): 53-65.

Asbtract ( 11 )

Related Articles | Metrics

In recent years, the "postgraduate entrance exam fever" has become a hot topic in public discourse. The contradiction between the supply of talent cultivation in higher education institutions and societal demands has become increasingly prominent. Therefore, it is crucial to guide graduates in rationally understanding the future trends of postgraduate entrance exams, and the quantity of master's enrollment is a key factor influencing whether undergraduates choose to apply. Based on the three-parameter discrete grey forecast model, this paper introduces dynamic background value and a time delayed power term to construct a time delayed discrete grey power model (TDDBGM(1,1,λ,tα). With the goal of minimizing the MAPE of total test, the PSO (Particle Swarm Optimization) algorithm is employed to globally optimize the parameters λ and α. Subsequently, this model is used to simulate and forecast the quantity of master's enrollment under the background of higher education popularization. The results demonstrate superior performance with train set error (3.28%), test set error (1.39%), and total set error (2.94%), all of which are significantly lower than those of the TDDGM(1,1,tα) model, DBGM(1,1) model, GM(1,1,t2) model, ARIMA model and SVR model. Based on the results, this
study proposes relevant policy recommendations.

Forecasting ICT Service Export Trends Using Advanced Grey Models

Saima Khan, Ghulam Abbas Bhatti, Muhammad Nawaz, Naiming Xie, Weiliang Zhang

2025, 37(6): 66-78.

Asbtract ( 16 )

Related Articles | Metrics

The study aimed to forecasts the future trends of information and communication technology (ICT) service exports in the United States of America (USA), China, India, and. By using the data obtained from the world bank, the study compares classical time series model that is exponential triple smoothing (ETS) with advanced grey-models including DGM(1,1,α), EGM(1,1), EGM(1,1,α,θ). ICT services are projected to be exponential in case of China and India, whereas for the USA, growth is projected to be approximately linear. EGM (1,1,α,θ) demonstrated superior performance in all three countries, as confirmed by the lowest mean absolute percentage error (MAPE). The additional parameters α and θ are likely to enable a more accurate representation of the underlying pattern in data, particularly in cases with significant fluctuations in data. The results have important implications for strategic planning in the digital infrastructure.

An Interval Grey Number Approach to Congestion Measurement in Data Envelopment Analysis

Chong Li, Xintian He, Xinru Yu

2025, 37(6): 79-90.

Asbtract ( 13 )

Related Articles | Metrics

Efficiency measurement in traditional Data Envelopment Analysis (DEA) models depends mainly on sampling, and the reliability of efficiency results is directly affected by the data quality of the Decision-making Units (DMUs). The interval DEA models have been developed to address the problem of inaccurate data in DEA. However, this study reveals that the existing models and approaches may lead to inaccuracies and inconsistencies in the measurement of efficiency and congestion effect. To address these shortcomings, this paper first proposes a new interval grey number envelopment model which takes into account the cross-evaluation logic between DMUs in an uncertain environment. It then proposes a novel algorithm for identifying and measuring the effects of congestion. The new method reserves the maximum possible range of efficiency values and improves the congestion identification between DMUs. Finally, the advantages and improvements of the proposed method are illustrated by several numerical examples.

A Novel Nonlinear Discrete Grey Bernoulli Model with Time Power Term and Its Applications#br#

Changyu Cai, Wenqing Wu, Mengfan He, Lianlian Luo

2025, 37(6): 91-111.

Asbtract ( 19 )

Related Articles | Metrics

The nonlinear grey Bernoulli model is a powerful grey forecasting model for analyzing nonlinear small sample sequences, which receives a considerable amount of interest in recent years. However, the inconsistency between its grey basic form used for linear parameters estimation and its grey differential equation used for time response function may cause large errors in some real applications. Thus this paper designs a nonlinear discrete grey Bernoulli model with time power term, abbreviated as NDGBM(1,1, ta), to improve the model accuracy. The expressions of the time response function and the linear system parameters are derived with the linearized form of the NGBM(1,1, ta) model. The structural parameters of the new discrete model are searched by the whale optimization algorithm. Further, according to historical data of gross regional product of Shifang city and Mianzhu city in Sichuan province, different type of continuous and discrete grey forecasting models are built, and the future values of selected cities are calculated.

Occupational Hazards and Workplace Safety in Organizational Setting: Grey Relational Evaluation#br#

Dongrui Xia, Mian Aziz Hussain, Xiaodong Ding, Razia Anjum, Beenish Ramzan, Muhammad Wasif Hanif

2025, 37(6): 112-123.

Asbtract ( 19 )

Related Articles | Metrics

With a view to improve health and safety of human resources in industry, the study aims to identify and evaluate the occupational hazards relevant to cement industry in China. Primary data were collected from the cement industry professionals based on physical, chemical, biological, process, and ergonomic and environmental hazards. The Dynamic Grey Relational Analysis (DGRA) was used to identify and rank the hazards. This method established an effective system to handle complex relations together with uncertainties found in occupational hazard information. For comparative analyses, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and the Grey Ordinal Priority Approach (OPA-G) were used. We found that the most significant hazard was physical cement dust in all methods. The Kruskal-Walli’s test (KWT) was also applied to investigate the significance of this hazard across different demographics groups, and found no significant differences among them. This study is the first of its kind to apply the Grey Relational
Analysis methods to explore the occupational hazards of airborne contaminants in cement industry of China. This suggests the industry stakeholders to develop effective safety measures for the cement industry by correct identification and control of key hazards.

A New-information-prioritized Grey Bernoulli Model for Forecasting the Number of Students Enrolled in Higher Education of Chinese Provincial Administrative Regions#br#

Feifei Wang, Weizhen Zuo, Weijie Zhou

2025, 37(6): 124-136.

Asbtract ( 8 )

Related Articles | Metrics

Accurately forecasting the number of enrollments in higher education in China can optimize the allocation of educational resources and ensure the sustainable development of the education system. Unlike existing grey prediction modeling approaches, this paper proposes a novel concept, i.e., the accumulated generating sequences preserve morphological features similar to the original data while enhancing sequence smoothness, and build a novel New-Information-Priority Grey Bernoulli Model (NIPNGBM) for predicting the number of students enrolled in higher education with different trends. Then, we use the number of students enrolled in higher education per 100,000 population from 2010 to 2021 in Beijing, Guangxi, Xizang, and Ningxia as examples, testing the adaptability of the new model to various sequence patterns, such as L-shaped, rising, inverted U-shaped, and S-shaped sequences. And the last block validation method in sample segmentation is used for hyper-parameters optimization. Results indicate that the proposed model demonstrates higher prediction accuracy and lower prediction volatility, compared against LSTM, Holt-Winters, ARIMA, LSSVR, and NGBM models. Furtherly, the new model is applied to forecast and the development trends of the number of students enrolled in higher education across 31 provinces in mainland China in the next seven years are analyzed from different time points, population thresholds, and different regions. This concept that grey prediction models balance both the shape and smoothness of the original sequence can be extended to the grey predictive modeling system, making the cumulative generation and the construction of new model more compatible, thereby expanding the application scope of the model.

Table of Content