Table of Content

25 September 2026, Volume 38 Issue 4

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Governance, Security, and Public Satisfaction: Evidence from Romanian and Moldovan Regions through Grey Clustering Analysis

Camelia Delcea, Rafal Mierzwiak, Constantin Marius Profiroiu, Alina Georgiana Profiroiu, Bianca Cibu, Ionuț Nica, Ioana Ioanăș, Andra Sandu

2026, 38(4):  1-26. 

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This study investigates how varying the analytical emphasis placed on political and security-related indicators shapes citizen satisfaction at the regional level in Romania and the Republic of Moldova. In a socio-political environment characterized by institutional transformation and evolving security challenges, identifying the combined and separate effects of these dimensions is critical for designing effective regional policies. The empirical analysis employs a grey clustering methodology to classify counties into three distinct satisfaction categories. To capture the sensitivity of outcomes to indicator prioritization, five predefined analytical configurations are constructed, reflecting different emphases on political versus security factors. The results show that under political-dominant configurations (100% or 80%), a larger share of Romanian counties (22–24 out of 42) are classified in the highest satisfaction cluster, while Moldovan counties are predominantly located in the lowest cluster. Conversely, under security-dominant configurations (80% or 100%), between 23 and 28 Moldovan counties are assigned to the highest satisfaction cluster, whereas 36–37 Romanian counties shift to the lowest cluster. These consistent structural shifts across predefined analytical configurations highlight the context-dependent role of governance and security perceptions in shaping regional satisfaction patterns.

Traction Elevator Operational Status Evaluation Based on Grey Clustering with Center-Point Possibility Functions

Shangbing Wu, Jun Han, Guolong Yao, Yanfei Kou, Tengyu Li, Jianxin Wang

2026, 38(4):  27-37. 

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Accurate evaluation of traction-elevator operational status is important for condition monitoring and maintenance decisions. However, conventional discrete classification may lose transitional information when operational indicators approach state boundaries. To address this issue, this study proposes a grey clustering evaluation method based on center-point possibility functions. A 17-indicator evaluation framework covering eight functional subsystems is established, and heterogeneous measurements are transformed into a unified dimensionless deterioration scale according to their indicator attributes. Center-point possibility functions are then constructed to characterize gradual transitions between adjacent grey classes, while CRITIC is employed to determine objective indicator weights. A grade-continuous-index dual output is further introduced to provide both categorical classification and continuous deterioration characterization. A case study of five traction elevators shows that all evaluated elevators are classified as Excellent, while the continuous status index further distinguishes their operational conditions as E2>E1>E3>E4>E5. Comparison with hard grey-class assignment demonstrates that the proposed representation retains transitional information near class boundaries and provides additional discrimination among elevators within the same dominant grey class. The proposed method provides a more informative representation of traction-elevator operational condition.

Prediction and Analysis of Trade Index between China and the Countries of Belt and Road Partner with an Improved Grey Model

Chen Chen, Bo Zeng

2026, 38(4):  38-50. 

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The Trade Index published by the General Administration of Customs of China is an important composite indicator for tracking trade dynamics under the Belt and Road Initiative (BRI). However, the annual series is short and exhibits considerable uncertainty and structural variation, which limits the applicability of data-intensive forecasting methods. To address this issue, this study develops a dual-parameter-optimized DGM(1,1,r,ξ) grey prediction model by jointly estimating the fractional accumulation order r and the background-value coefficient ξ. Using annual Trade Index data for China and Belt and Road partner countries from 2013 to 2023, the empirical results show that the proposed PSO-optimized DGM(1,1,r,ξ) model achieves the lowest comprehensive percentage error (0.91%) among the competing grey models. Compared with the single-parameter DGM(1,1,r) model, the improvement is slight, but the proposed model still provides the best overall balance between in-sample fitting and out-of-sample prediction under the unified evaluation framework. These results suggest that the joint optimization of r and ξ can improve predictive performance in a small-sample and policy-sensitive setting. This study provides an empirically grounded grey modelling framework for Trade Index forecasting and a quantitative reference for analyzing trade dynamics under uncertainty.

A Unified Evaluation Framework for Optimization Strategies in Grey Forecasting: Evidence from the Conformable Fractional GM(1,1) Power Model

Shuanghua Liu

2026, 38(4):  51-63. 

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Whether different improvement mechanisms in grey forecasting models can provide stable out-of-sample forecasting gains under small-sample conditions requires evaluation under consistent settings. Using China’s national average overall digital finance index from 2011 to 2023, this study develops a unified evaluation framework to compare GM(1,1), the GM(1,1) power model (GPM), the conformable fractional GM(1,1) power model (CFGPM), and three CFGPM extensions based on initial-condition optimization, background-value optimization, and logarithmic transformation. The models are evaluated using a rolling-origin expanding-window approach, sensitivity analysis of the initial estimation window, and the exact Wilcoxon signed-rank test. The out-of-sample MAPEs of GM(1,1), GPM, and CFGPM are 12.08%, 3.49%, and 2.96%, respectively. The CFGPM also has a lower Median APE than the GPM, although their paired forecast-error difference is not statistically significant. In contrast, the difference between the CFGPM and GM(1,1) is significant at the 5% level. The three additional optimization strategies reduce errors at some forecast origins but provide neither a stable overall advantage over the CFGPM nor a statistically significant improvement. The sensitivity analysis gives the same main comparative results. Overall, the power-function structure and conformable fractional accumulation are associated with lower out-of-sample forecast errors, while further optimization does not necessarily produce stable forecasting gains. Re-estimating the CFGPM with all observations from 2011 to 2023 shows that China’s national average overall digital finance index is expected to continue increasing from 2024 to 2027, with gradually smaller annual increments.

Optimizing Satellite Access Selection in GEO-LEO Heterogeneous Satellite Networks: A Grey Clustering Enhanced Proximal Policy Optimization Algorithm

Shuang Wu, Zhigeng Fang, Liangyan Tao

2026, 38(4):  64-76. 

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To address the satellite access problem in geostationary earth orbit and low earth orbit (GEO-LEO) heterogeneous satellite networks characterized by periodic satellite motion and time varying user demands, this study develops a grey clustering enhanced proximal policy optimization (GC-PPO) method with invalid action masking. First, a GEO-LEO heterogeneous satellite networks is established and key state attributes are modeled based on satellite networks (SNs) characteristics. A grey clustering model is introduced to generate grey clustering coefficients reflecting heterogeneous satellite conditions and user preferences. These coefficients are used as unified observations for the reinforcement learning agent and are further incorporated into action masking to eliminate infeasible decisions. The integration of grey clustering model with proximal policy optimization improves decision efficiency, and neural network approximation in DRL enables implicit weighting of grey clustering coefficients, providing an adaptive mechanism for handling similarities among satellite state representations. Simulation results demonstrate that the proposed strategy reduces blocking and handover rates while improving quality of service (QoS).

An Input-Output Performance Evaluation GRCD∙TOPSIS Method with Limited Decision-Making Units — Based on the Data of Regional Universities in China

Songyang Zhang, Changcheng Li, Xiaomin Shen, Fang Wang

2026, 38(4):  77-85. 

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This study develops a CRITIC-weighted Grey Closeness Relational Degree-based TOPSIS (GRCD∙TOPSIS) method for evaluating input-output performance under small-sample conditions with a limited number of decision-making units (DMUs). To enhance comparability, the original input and output data are adjusted for variations in system scale and transformed logarithmically. The CRITIC (Criteria Importance Through Intercriteria Correlation) method is applied to determine objective weights for input and output indicators separately. Within the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) framework, positive and negative ideal solutions are established based on the cost-type nature of inputs and the benefit-type nature of outputs. Grey closeness relational degrees to the ideal solutions are computed from CRITIC-weighted absolute distances and subsequently synthesized to yield input and output scores, with overall efficiency measured as the ratio of the output score to the input score. An empirical study of higher education systems across 31 provincial-level regions in mainland China demonstrates that the proposed method effectively differentiates provincial efficiency under limited-DMU conditions and reveals significant regional heterogeneity in input, output, and conversion efficiency. At the regional level, the Northeastern region exhibits the highest efficiency, followed by the Western, Eastern, and Central regions. The approach offers a transparent and data-adaptive tool for small-sample input-output performance evaluation, with promising applicability in contexts where conventional DEA-like methods are infeasible due to sample size constraints.

Interval Grey BP Neural Network Combinatorial Model with Time-delayCausal Term and its Applications

Jing Ye, Luolan Zhang

2026, 38(4):  86-98. 

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As the complexity of the system increases, real numbers often fail to capture the inherent uncertainty in the data. However, time delay and nonlinear interdependence pose further challenges to accurate modeling. To address these issues, this paper thoroughly investigates the time-delayed and nonlinear effects of related factor sequences on system behaviour sequences within the interval sequence framework, and proposes an interval grey BP neural network combination model with time-delay causal term, named BP-TDIGM(1,1). Firstly, considering the uncertainty and time-delay characteristics of data, this study integrates model and introduces a time-delay parameter, extending the traditional time-delay prediction model to an interval time-delay prediction model. The Kramer method is then employed to solve the proposed model. Secondly, combined with the BP neural network, a serial grey BP neural network hybrid model is constructed to characterize the nonlinear impacts of related factor sequences on system behaviour sequences. Subsequently, the least squares method and particle swarm optimization algorithm are utilized to determine the structural parameters and time-delay parameters of the model, respectively. Finally, the effectiveness of BP-TDIGM(1,1) is verified through fitting and prediction experiments on two numerical examples and a practical case concerning R&D expenditure in the Yangtze River Delta. The results are compared with six other grey prediction models, demonstrating that the proposed model outperforms other grey models in terms of prediction accuracy for multivariable interval time-delay data series.

Performance Evaluation of Natural Rubber Origins for Aviation Tire Components Using Grey Relational Analysis

Kun Jiang, Baoling Wang, Honghao Zhao

2026, 38(4):  99-110. 

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This study aims to establish a data-driven decision framework for selecting natural rubber (NR) in aviation tire formulations, in order to overcome the problem of long-term reliance on empirical knowledge and enhance the ability to autonomously select materials for high-end equipment. A multi-dimensional simulation performance database was constructed, covering six mainstream NR brands from six major production areas, namely Malaysia (MYS), Indonesia (IDN), Thailand (THA), Vietnam (VNM), Hainan (CHN), and Yunnan (CHN), which were selected based on market dominance and traceability in the literature. This database integrates the raw material rubber composition, molecular parameters, and static or dynamic mechanical properties of the vulcanized rubber. Grey Correlation Analysis (GRA) was introduced as the core decision model. By calculating the grey correlation grade between each NR brand and the ideal reference sequence based on the target performance indicators, the multi-criteria ranking of different functional components of aviation tires (such as tread, shoulders, sidewalls, and carcass) and differentiated material recommendations were achieved. To verify the reliability of the model, it was first applied to the mature main landing gear tires of the Boeing 737-800 aircraft, and the model output results were compared with the material usage records of a well-known international tire manufacturer. In the verification case, Malaysia's SMR CV60 was determined as the optimal choice for the tread, shoulders, and sidewalls, and Vietnam's SVR 3L was the optimal choice for the carcass. Its performance fully matched the parameters of the ideal performance sequence, thereby confirming the reliability of the model. Subsequently, the validated model was applied to the main tires of the Chinese C919 aircraft. For the C919 main tires, the model recommended Malaysia's SMR CV60 as the best material for the tread, shoulders, and sidewalls, while SVR 3L demonstrated superior overall performance in the carcass composite material. This framework provides a scientific material selection basis for the C919 main tires, reveals the potential for substitution of domestic NR materials in specific tire components, and offers a transparent and quantifiable alternative solution for the decision-making of high-performance tire formulations, replacing the traditional empirical decision-making. Its innovation lies in combining the specially constructed performance database with GRA (tire formulation analysis system) to achieve a data-driven decision-making method. It provides the first data-based natural rubber selection suggestion for the C919 main tires and systematically demonstrates the feasible ways to substitute domestic natural rubber in key aviation components.

Multi-objective Performance Optimization of Rubber Composites: An Integrated Framework Based on Grey Relational Analysis and Orthogonal Experiments

Anqi Li, Liangyan Tao, Xianhui Zhang, Sifeng Liu, Fernando Acebes

2026, 38(4):  111-124. 

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Rubber composite formulation design requires the simultaneous optimization of multiple properties, whereas orthogonal experiments are often limited by small sample sizes and responses with different dimensions and optimization directions. To address this issue, this study proposes a multi-objective performance optimization framework based on grey relational analysis and orthogonal experiments. First, the multi-response orthogonal experiment optimization problem is formally defined, and an integrated procedure involving response normalization, reference sequence construction, grey relational analysis, and signal-to-noise ratio optimization is established. Second, equal-weight and weighted grey relational models are developed, with their applicability examined through weight sensitivity analysis and index permutation invariance. The results indicate that point-to-point grey relational methods are more suitable for evaluating parallel performance indicators. The proposed framework can identify promising formulation regions within a limited experimental space and provide interpretable guidance for key-variable selection and subsequent extrapolation, making it suitable for small-sample, multi-factor, and multi-objective optimization of rubber composites.

Remaining Useful Life Prediction for Lithium Batteries Using a Recursive Non-homogeneous Grey Model with Online Anomaly Detection

Zhicun Xu, Huakang Diao

2026, 38(4):  125-133. 

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Accurately predicting the remaining useful life (RUL) of lithium batteries is crucial for ensuring reliable equipment operation, mitigating safety risks. This is of great significance for advancing the new energy industry. To improve the adaptability of grey model to the lithium battery aging process, a recursive least-squares parameter estimation method is incorporated into the non-homogeneous grey model. By incorporating the latest operational data from lithium batteries in real time, the model parameters are updated recursively, effectively tracking the dynamic patterns of lithium battery aging. This paper validates the proposed model using the University of Oxford’s public lithium battery dataset. To address the issue of sudden capacity failure in lithium batteries, we propose an online abnormal detection method based on sliding window residual statistics and modify the recursive non-homogeneous grey model. The results indicate that this proposed model can accurately predict the remaining useful life of lithium batteries, demonstrating good predictive accuracy and stability. It is capable of meeting the requirements for predicting the RUL of lithium batteries in practical engineering applications