Table of Content

20 July 2026, Volume 38 Issue 3

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A Novel Time-varying Grey Model for the NEV Sales Prediction in China

Shuliang Li, Rongji Zhang, Guijun Zhang, Xun Zhang, Mingmeng Gan, Liangping Zhang

2026, 38(3):  1-15. 

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Current time-varying grey models generally suffer from structural rigidity and insufficient consideration of the intervention effect. To further broaden the application scope of time-varying grey models, this paper proposes a novel fractional time-varying discrete grey model based on the intervention effect (IE-FTVDGM(1, N)). The new model reconstructs the time-varying term by introducing a fractional-order time series to construct a grey model with an adaptive time-varying structure. The reconstructed time-varying term combines integer-order and fractional-order polynomial properties, and can be flexibly adjusted by optimizing a single hyperparameter. In addition, the dual carbon policy is incorporated into the modeling framework as an intervention dummy variable to capture anomalous fluctuations.To determine the optimal hyperparameters, we select the particle swarm algorithm after comparing it with other intelligent algorithms. Finally, Monte Carlo is used to evaluate the robustness of the proposed model. When applied to forecasting China’s new energy vehicle sales, the proposed IE-FTVDGM(1, N) achieves an MAPE of 0.101% and an R2 of 0.9999. It consistently maintains an MAPE below 1% under three different noise levels, demonstrating superior accuracy and stability over all competing models.

Grey Relational Analysis for Multi-Response Optimization of Drilling Parameters in GFRP Composites

Mohamed S. Abd-Elwahed

2026, 38(3):  16-26. 

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This study focuses on the multi-objective optimization of drilling parameters—specifically feed and spindle speed—for chopped glass fiber reinforced polyester (CGFRP) composites with varying fiber volume fractions. To enhance machining efficiency, drilled hole quality, and energy performance, key output metrics, including material removal rate (MRR), delamination size, thrust force, and drilling torque, were evaluated. A hybrid optimization technique integrating Grey Relational Analysis (GRA) with Principal Component Analysis (PCA) was employed to systematically balance and improve these performance indicators, supporting a more sustainable drilling process. Analysis of variance (ANOVA) is used to determine the most influential parameters for machinability properties, delamination size, and grey relational grade (GRG). Results revealed the feed as the most influential control factor on weighted GRGw. The optimum drilling parameters for the multi-objective optimization were a feed of 0.08 mm/r for all fiber volume fractions in the composite and a spindle speed ranging from 875 to 1850 rpm as fiber volume fractions ranged from 0.16 to 0.27.


A Time-delay Grey Relational Analysis Model based on Procrustes Distance

Honghua Wu, Aqin Hu, Yafang Li, Xue Han, Yang Li

2026, 38(3):  27-35. 

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To address the issues in existing panel data-based grey relational analysis models (PD-GRA), such as the neglect of indicator’s time delay and data transformation considerations, a time-delay grey relational analysis model (TDGRA) is proposed. First, the concepts of the sample matrix, the submatrix under time delay, and the corresponding truncation matrix are introduced. Second, singular value analysis is performed on the relevant matrices, and the optimal rotation matrix is derived. Then, an optimization model is constructed with the goal of minimizing the Procrustes distance, through which the time delays between indicators are determined. And then, a PD-GRA model is proposed based on the optimal Procrustes distance with time delay. Finally, the TDGRA model is used to identify the driving factors of AQI in the Yellow River Basin, obtaining urbanization rate (UR), carbon emissions (CE), gross domestic product (GDP), and the growth of total investments in fixed assets (GIFA) as the main drivers. The results demonstrate the rationality and effectiveness of the proposed TDGRA model, and its advantages are further highlighted through comparative analysis.





A Laguerre Polynomial Grey Model with Non Conformable Fractional Derivative for Energy Consumption Forecasting

Meixin Huang, Jianguo Zheng

2026, 38(3):  36-46. 

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Energy consumption consistently exhibits pronounced non-linearity, making trend prediction difficult when only limited samples are available. To overcome this challenge, we employ Laguerre polynomials to construct a novel grey forecasting model that integrates fractional difference and accumulation. Empirical results show that the proposed model outperforms alternative approaches in accuracy, stability, and applicability. The proposed model, optimized via particle swarm optimization, manifested superior forecasting precision for energy consumption in Heilongjiang, Jiangsu, and Xinjiang, with mean absolute percentage error values of 5.225%, 4.098%, and 4.392% respectively. This performance conspicuously surpassed five traditional grey system models and two machine learning models, accentuating the robustness and exactitude of the model in capturing regional crude oil consumption patterns and trends. Furthermore, the newly proposed model was applied to a representative set of major oil-consuming economies, and, for every country considered, the out-of-sample forecasts remained below 10% error, underscoring the model’s robustness and its practical utility for global energy-demand planning.





Understanding AI Acceptance Among China’s Disabled Elderly: A Novel Grey Relational Model

Kune Zhao

2026, 38(3):  47-62. 

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This study develops a validated, disability-inclusive acceptance framework for AI-assisted elder care systems, addressing a critical gap by focusing on the underrepresented perspectives of older adults with disabilities in China. Through a rigorous three-stage methodology, synthesizing aging-technology and disability studies literature, expert co-design with specialists in gerontology, human-computer interaction, AI ethics, and disability advocacy, and participatory piloting, we established a multidimensional framework of six criteria and eighteen sub-criteria. Survey data from 238 elderly participants with visual, hearing, motor, and cognitive impairments across three Chinese cities were analysed using the novel GSRA, TOPSIS for validation, and Kruskal–Wallis H tests for subgroup analysis. Results identify Emergency Response Reliability (GRG = 0.811; "S" _"i"  "=0.719" ; "w" _"i"  = 28.5%) as the paramount trust factor, followed by Interface Simplicity and Voice & Multimodal Interaction Quality. Contextual factors like infrastructure and family support were consistently deprioritized. Importantly, the Kruskal–Wallis test revealed trust perceptions are significantly influenced by disability type (H=18.73, p<0.001), with motor-impaired users placing highest importance on emergency reliability. Strong agreement between GSRA and TOPSIS confirms the robustness of the findings. We conclude that trust is fundamentally built through the AI system's own functional reliability and accessible design, not external conditions. The study offers an evidence-based, culturally informed framework to guide the creation of equitable, trustworthy, and disability-inclusive AI systems for aging populations, contributing to both aging-technology design and the practical application of grey system theory.





Mitigating Surgical Duration Bias in Operating Room Scheduling with a Grey Possibility Function-Based Multi-Model Fusion Framework

Zongli Dai, Zuli Pi, Peng Jiang

2026, 38(3):  63-75. 

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For the insufficient prediction accuracy and systematic bias in traditional single machine learning model for elective surgery scheduling, this study innovatively proposes a multi-model fusion framework based on the grey possibility function, which improves prediction accuracy through a grey possibility-function-based representative fusion mechanism. A grey representative prediction system was constructed by integrating machine learning algorithms such as gradient boosting, random forest, and decision trees. Notably, this system introduces an innovative three-layer surgical duration classification framework that autonomously adjusts prediction parameters based on the characteristics of surgical durations. This feature effectively addresses the traditional model’s tendency to underestimate long surgeries and overestimate shorter ones. In the verification phase, multidimensional evaluation is conducted using prediction accuracy indicators and scheduling efficiency indicators. Experimental data shows that the new framework achieves a 0.13% reduction in MAE indicators and a 3.0% increase in R². In terms of surgical scheduling efficiency, the average total overlap time was optimized to 8.81 minutes, a decrease of 36.48%. More importantly, the prediction bias of long and short surgeries narrowed to -14.2% and +45.4%. This research provides reliable data support for the allocation of operating room resources. By accurately predicting the surgery duration, it can improve the utilization rate of operating rooms, optimize the scheduling of medical staff, and rationalize the scheduling of medical equipment, ultimately promoting the overall improvement of medical service quality.





A New Time-varying Oscillatory Fractional-order TFOGM(1,N,r_i ) Power Model and its Application

Ye Li, Tianqi Jin, Huimin Zhou, Li Han

2026, 38(3):  76-92. 

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To address the prediction of time series characterized by periodic oscillation, nonlinear trends, and uncertain system behavior, this paper proposes a novel time-varying oscillatory fractional-order TFOGM(1,N, ) power model. Firstly, it adaptively adjusts the accumulation order of independent and dependent variables based on fractional-order calculus. Secondly, trigonometric functions with integer rounding and time power terms are introduced to capture the oscillatory and nonlinear features of the time series, while dummy variables are utilized to quantify policy impacts. Subsequently, by comparing various intelligent algorithms, an optimal algorithm is selected for global hyperparameter optimization. Finally, the model accuracy is validated through a core case study on monthly carbon dioxide emissions in China, supplemented by a case on quarterly solar power generation. Empirical results show the model significantly outperforms comparative models in accuracy, robustness and generalization, with excellent practicality and reliability.

An Improved Grey Power Model with Optimized Exponent and Its Engineering Applications

Yiyuan Zhu, Jiaqi He, Hanyue Wang, Wenjie Dong

2026, 38(3):  93-107. 

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The grey power model captures nonlinear trends, but its accuracy heavily depends on the power exponent, which is often empirically selected. For instance, the grey Verhulst model and GM(1,1), two special  cases of grey power models and widely applied,  struggle to adapt to the fitting of complex data. To address this, we propose an Improved Grey Power Model (IGPM) that optimizes the exponent γ via a dual-path optimization strategy integrating grid search and the Artificial Fish Swarm Algorithm (AFSA) within the theoretically determined bounds of [-2, 2]. In the context of small-sample data, validated on annual power generation and metal fatigue strength, the optimized IGPM reduces MAPE by 37.5% and RMSE by 38.0% on average over the standard GM(1,1). The framework provides a robust solution for data-scarce engineering predictions.

A Preference-learning UTilités Additives Method for Three-parameter Interval Grey Numbers with Inconsistent Preference Information

Peng Li, Mengke Liu, Jian Liu

2026, 38(3):  108-117. 

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Preference learning is one of the important methods in machine learning and has been applied in various fields. Preference learning in the presence of uncertain information is still a field that deserves further attention. The main objective of this paper is to construct a preference learning model for three‑parameter interval grey numbers (TPIGNs) using the UTilités Additives (UTA) method, to solve two key issues in preference learning: (1) failing to find the optimal preference, and (2) having multiple optimal preferences complicates the selection process. To address the two issues, this paper proposes a preference-learning method based on the UTA model for TPIGNs considering the inconsistent decision maker's pairwise preferences. TPIGNs are first converted into whitening values under a triangular possibility distribution and then incorporated into an additive value-function model. The first-rank acceptability index from stochastic multicriteria acceptability analysis (SMAA) is used to measure the prior importance of each reference alternative, from which an importance index is defined for each pairwise preference constraint. An improved UTA model is then constructed to identify and remove low-importance contradictory preferences through binary variables while retaining more informative preference statements. A random-direction extreme-point sampling procedure is used to obtain representative value-function parameters and improve the robustness of the ranking result. A supplier-selection case involving age-friendly equipment illustrates the implementation of the method and its advantage over the traditional UTA method in handling inconsistent preference information.

Integrating Sustainability, Circular Economy, and Industry 4.0 Criteria in ERP Software Selection using Grey MCDMs

Mustafa Said Yurtyapan, Erdal Aydemir

2026, 38(3):  118-133. 

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Selecting an enterprise resource planning (ERP) system that simultaneously satisfies sustainability, circular economy, and Industry 4.0 requirements is a multi-criteria decision problem complicated by incomplete information and small expert panels, in which judgments are more naturally expressed as ordinal priorities than as precise scores. To address the lack of an integrated sustainable-ERP (S-ERP) selection framework for these conditions, this study develops and applies a Grey System Theory (GST)–based Grey Ordinal Priority Approach (OPA-G). The framework embeds sustainability, circular economy, and Industry 4.0 criteria in a single decision structure and represents the judgments of a three-member expert panel as ordinal priorities under grey interval uncertainty, avoiding pairwise comparisons while preserving uncertainty through grey numbers. The model is applied to a real manufacturing case, and its robustness is tested through seven expert-priority scenarios together with area-level (±10%, ±20%) and ordinal perturbation analyses, and benchmarked against Grey TOPSIS and Grey VIKOR. The results show that the Fundamental and Economic criteria dominate the decision (0.640), followed by Industry 4.0 compatibility (0.233), environmental (0.099), and social (0.028) criteria; System Cost, Quality, and Financial Situation are the most influential criteria, while Cloud and Edge Computing, Artificial Intelligence, and IoT are the leading digital requirements. The framework yields the ranking ERP1 > ERP2 > ERP3 > ERP4, which remains unchanged across all perturbation scenarios and is reproduced identically by Grey TOPSIS and Grey VIKOR. Although economic performance remains primary, Industry 4.0 capabilities are the decisive enablers that make environmental and social monitoring operationally executable. The proposed framework therefore offers a transparent, robust, and practically implementable decision-support tool for sustainable ERP procurement under uncertainty, extensible to multi-firm panels and broader sustainability domains.