A key property of grey prediction models is their unbiased nature, which focuses on eliminating discontinuity between differencing and differentiation during their construction. Meanwhile, an unbiased proof is required to ensure this property. In this paper, an unbiased EDGM(1,1) model incorporating Euler polynomials is constructed. Firstly, this model integrates Euler polynomials and a time disturbance parameter into the classical GM(1,1) model, enabling this EDGM(1,1) model to flexibly handle sequences with various data characteristics. Subsequently, the difference and its discrete forms are derived, and the latter is then solved using the least squares method and mathematical induction. Then the Particle Swarm Optimization (PSO) algorithm is implemented to improve the model's parameters. Secondly, the compatibility of the EDGM(1,1) model is demonstrated, and its unbiasedness towards three characteristic sequences is proven based on Cramer's rule. Finally, the performance of the EDGM(1,1) model is evaluated comprehensively against five competing models using three metrics: MAPE, RMSE, and R². The comparative analysis shows that the EDGM(1,1) model outshines other models in robustness and accuracy. Furthermore, the novel model is designed to forecast China's primary energy outputs, aiming to provide references for energy policies and decision-making. 

Every recommendation engineer needs to face the cold start problem when building his system. During the past decades, most scientists adopted transfer learning and meta learning to solve the problem. Although notable exceptions such as ZeroMat etc. have been invented in recent years, cold-start problem remains a challenging problem for many researchers. In this paper, we build a zeroshot and privacypreserving recommender system algorithm GreyShot using GM(1,1) model by taking advantage of the Poisson-Pareto property of the online rating data. Our approach relies on no input data and is effective in generating both accurate and fair results. In conclusion, zeroshot problem of recommender systems could be effectively solved by grey system methods such as GM(1,1). 

Accurate prediction of port throughput is critical for enhancing the precision of port construction decisions. However, identifying the factors influencing port throughput and constructing a robust predictive model remain significant challenges. To address this issue, this paper develops a modeling framework based on grey systems theory. First, grey relational analysis is employed to identify the relevant factors impacting changes in port throughput. These influencing factors are then utilized to construct a multivariate weighted fractional grey model for throughput prediction. To enhance the predictive capability of the grey model, this study establishes an error-based objective function to determine the model's fractional order, followed by corrections to the residual sequence using Long Short-Term Memory (LSTM) neural networks to improve prediction accuracy. To validate the effectiveness of the proposed method, empirical analysis is conducted using port throughput data from Guangxi Province, with comparisons made against four commonly used models. The experimental results demonstrate that the grey modeling framework proposed in this paper achieves high accuracy, with a 0.67% reduction in mean absolute percentage error (MAPE) outperforming alternative models. Furthermore, the model predicts a rapid growth trend in port throughput in Guangxi over the next three years, suggesting that expanding the utilization rate of existing port infrastructure and accelerating investments in capacity expansion are critical for meeting future demand. These results highlight the model's potential as a decision-support tool for strategic planning in the port and logistics sectors. 

Carbon emission projections are pivotal in addressing global climate change and advancing green, low-carbon development. Accurate forecasts of China's carbon emissions provide critical insights for policymakers to understand future emission trends and potential peak levels, thereby enabling the formulation of scientifically grounded and practical mitigation strategies. Discretization has proven to be an effective approach for enhancing the accuracy of grey prediction models. To further refine the performance of discrete grey prediction models, this study integrates integer-order polynomials with time fractional power terms to develop an optimized discrete grey prediction model, DGMPT(1,1,N, ), the particle swarm optimization (PSO) algorithm is utilized to optimize hyperparameters. To validate the model's superiority and predictive accuracy, this study applies it to the carbon emission data of Xinjiang, Shaanxi, and Gansu provinces in China. Empirical results demonstrate that, based on the mean absolute percentage error (MAPE) criterion, the proposed model achieves the lowest MAPE values in both the training and prediction datasets across all three case studies. Finally, the proposed model is employed to forecast China's carbon emissions over the next decade. The results indicate that under current conditions, China is unlikely to achieve its peak carbon emissions by 2030. This underscores the urgency of implementing effective and comprehensive policy measures to improve carbon emission systems and foster a sustainable emission environment. 

To address issues in the validation and analysis methods of panel data-based grey relational analysis models (PD-GRA), this paper introduces various validation methods for the PD-GRA model, including Collision Testing Analysis (CTA), Stability Testing Analysis (STA), Permutation Testing Analysis (PTA), Rolling Window Time Analysis (RWTA), along with corresponding visualization techniques. These approaches are designed to analyze the robustness of grey relational analysis model (GRA). First, the concepts of strong and weak collisions for the GRA model are defined, along with their occurrences at different levels. Conclusions on strong and weak collisions are drawn for different GRA formulas. Second, STA, PTA, and RWTA are systematically presented to evaluate the stability of PD-GRA model from different perspectives. Meanwhile, visualizations for these three tests are also provided. Finally, a simulation analysis is conducted to examine the collision behavior of traditional GRA models. A case study is then used to apply STA, PTA, and RWTA to the PD-GRA model, accompanied by visualizations, offering deeper insights into the model's performance. 

In order to improve the profit, reduce the shutdown loss and enhance the environment benefit, an optimization model of petrochemical energy manage system is established based on improved parallel moth flame optimization algorithm (IPMFOA). Firstly, the petrochemical energy management system optimization model is constructed, and the object function and constraint condition are confirmed. Secondly, an Grey-IPMFOA is established. Finally, an energy management system of refinery in a petrochemical company is selected as research object to carry out optimization analysis based on proposed Grey-IPMFOA and other three optimization algorithms, results show that proposed optimization can get best optimal effect and highest optimal efficiency. In addition, proposed Grey-IPMFOA has better convergence performance and computation complexity. The energy management system after optimization has high profit, low shutdown loss and high environment benefit. 

The conventional series system and parallel system are no longer able to adequately address the current system condition due to the rapid advancement of science. If faults are not identified and isolated, any system failure can lead to the inability to perform a single task or even multiple tasks. In order to promptly identify and isolate faults, the systems must have high testability. However, problems like omitting structural elements in testability influencing factors and ambiguous testability-related data make standard approaches useless when building and resolving testability allocation models. The grey optimization approach will lose a lot of grey information if a planning model is employed for solution, which will lead to large inaccuracies. Therefore, this paper proposes a testability allocation model for complex systems in the setting of grey information, and proposes the grey double-layer particle swarm optimization algorithm to solve the model. First, the particular factor that influence the testability allocation process is identified. Second, this paper proposes the TOPSIS method based on the improvement of grey entropy weight and determines the weights of the subsystems. Then, this paper proposes the grey nonlinear planning testability allocation model, and proposes the grey double-layer particle swarm optimization algorithm to solve the model. Finally, the viability and efficacy of the model are demonstrated by strength testing and comparison with other algorithms. 

This study investigates human resource crisis management in Offshore Engineering Design (OED) enterprises, focusing on the specific challenges faced by Chinese firms. The research develops a comprehensive early warning indicator system, integrating 15 qualitative and 21 quantitative indicators across five key dimensions. Given the limitations posed by insufficient data and inherent uncertainties in the evaluation process, this study also presented a grey evaluation method to construct a risk assessment model for OED human resource crises. A case study of AOED reveals critical issues, including inefficiencies in performance assessment and high staff turnover, underscoring the need for enhanced management strategies. The findings contribute to improving OED human resource management and provide a foundation for future research on predictive models in OED contexts.

This paper examines the impact of varying the significance of socio-economic and security indicators on the satisfaction levels of citizens across different counties in Romania and Republic of Moldova. Using grey clustering analysis, a powerful tool offered by the grey systems theory, the counties are grouped into three clusters based on citizen satisfaction. Five different scenarios are explored, each assigning distinct weights to socio-economic and security indexes to evaluate their influence on the clustering outcomes. The findings indicate that increasing the emphasis on socio-economic factors leads to more counties experiencing higher levels of citizen satisfaction, particularly in Romania, where socio-economic stability is more robust. On the other hand, placing greater importance on security factors exposes governance-related challenges, as a clear division between the counties in Romania and Republic of Moldova can be observed. While when considering the security indexes, more counties are pushed in the higher levels of satisfaction clusters for the counties in Republic of Moldova, an opposite trend can be encountered for the counties in Romania.