Purpose This study aims to address the issues of overfitting and underutilization of new information in traditional grey models for multi-frequency traffic flow forecasting. It proposes the Recursive Grey Multi-frequency Fourier Model (RGMFM) to enhance the extraction of multi-frequency periodic features and enable dynamic updating, thereby improving the accuracy and stability of short-term predictions for small-sample, multi-frequency traffic flow data. Design/methodology/approach The RGMFM integrates Fast Fourier Transform (FFT) and a recursive regression algorithm into the grey modeling framework. FFT extracts primary and secondary periodic components, while recursive regression prioritizes parameter updates with new data. The model incorporates two controllable parameters—an energy threshold and a memory factor—to simultaneously optimize its structure and parameter updating mechanism. Findings Simulation and experimental results demonstrate that RGMFM significantly outperforms benchmarks (SARIMA, LSTM, Transformer), reducing average RMSE by approximately 17% on 50 subsets of the PEMS08 dataset. It accurately captures daily and peak-hour traffic patterns and maintains robust performance under varying noise levels, validating its effectiveness and stability for multi-frequency forecasting. Originality/value The main originality lies in the novel hybrid framework that embeds signal processing (FFT) and recursive learning into grey system theory. The introduction of dual controllable parameters for integrated optimization provides a new, tunable, and interpretable modeling paradigm. This work extends grey models' applicability to complex, dynamic multi-frequency forecasting tasks, offering significant practical value for intelligent transportation systems and similar domains.
Purpose Accurate and reliable energy forecasting is fundamental to strategic decision making for the global transition toward decarbonization and digitalization. This paper proposes a novel nonlinear time-varying fractional grey multivariable model to address the limitations of conventional forecasting methods. Design/methodology/approach The proposed model offers a novel methodological improvement by integrating time-varying coefficients for dynamic parameterization, logarithmic adjustment terms for enhanced nonlinear modeling and a particle swarm algorithm for systematic optimization. Findings Empirical validation across municipal, provincial, and national case studies consistently confirms the superior predictive performance of the proposed model. Comparative analyses with benchmark models show that our model achieves the lowest prediction errors across all evaluation metrics. This outperformance remains robust in both training and testing phases. Practical implications The proposed approach provides a robust methodological framework for energy consumption forecasting, offering substantial improvements in accuracy and reliability for supporting energy strategy formulation and sustainable development planning. Originality/value Its originality stems from the integration of dynamic coefficients and logarithmic adjustment terms. This integrated framework effectively addresses the limitations of static parameters and fixed structures in conventional grey models.
Purpose Aiming at the issue that traditional multivariable grey prediction models cannot fully identify nonlinear trends among sequences, this paper introduces power-exponential and time-power-logarithmic correction terms, combines intelligent algorithms to flexibly optimize the model's unstructured parameters and proposes a new logarithmic flexible discrete grey LFDGM (1, N) model to deeply mine data sequence patterns and adapt to data development trends. Design/methodology/approach Firstly, nonlinear parameters are introduced into system behavior and relevant factor sequences, and a logarithmic time-power correction term is adopted to identify system nonlinear characteristics. Secondly, four mainstream intelligent optimization algorithms are compared to select the optimal one for hyperparameter global optimization with minimum average relative error. Then, the LFDGM (1, N) model is applied to fossil energy production prediction and compared with benchmark models. Finally, model stability is verified via Monte Carlo simulation and varying sample set experiments. Findings The experimental results show that the logarithmic flexible discrete grey LFDGM (1, N) model has better accuracy than other models in the global MAPE, verifying the validity and practicability of the model and indicating that this model has the optimal modeling effect on nonlinear complex systems. In addition, this paper verifies that the LFDGM (1, N) model has good robustness through Monte Carlo simulation and experiments with different sample sets. Practical implications Scientific and accurate prediction of fossil energy output is of great reference significance for China's formulation of energy industry plans and provides solid support for the long-term stable development of its energy industry. Originality/value To tackle complex, variable and highly uncertain system data sequences, this paper develops a logarithmic flexible discrete grey LFDGM (1, N) model. Embedding nonlinear power parameters in the system feature sequence and the related factor sequence, and introducing a logarithmic time-power correction term enhances nonlinear correlation depiction, captures early system abrupt changes and restricts late prediction divergence. Hyperparameters are optimized via preferred intelligent algorithms to improve prediction accuracy.
Purpose This study addresses the grey dynamic flexible job shop scheduling problem (GDFJSP), in which jobs with uncertain grey-number processing times arrive stochastically and must be dispatched in real time. It aims to develop a genetic programming algorithm that evolves interpretable heuristic dispatching rules while handling stochastic arrivals and iterative grey-time updating efficiently. Design/methodology/approach A memory-guided adaptive feature genetic programming (MGAFGP) algorithm is proposed with a dual-tree encoding for routing and sequencing decisions. The algorithm combines parallel simulation for concurrent fitness evaluation, an elite-memory-guided strategy with separate feature probability vectors for routing and sequencing trees, and a generation-dependent parent selection function. Its performance is evaluated across multiple scenarios defined by different objectives, utilization levels, and due-date tightness conditions. Findings MGAFGP reaches high-quality rules substantially faster than standard GP under the tested scenarios, showing corrected significant advantages during early evolution and reaching GP's full-budget mean performance with a substantially smaller iteration budget. No corrected full-budget comparison favours standard GP. The evolved rules outperform classical heuristic combinations after independent test re-evaluation, while feature-use patterns, symbolic expressions, and tree-complexity statistics show that the resulting dispatching logic remains inspectable. Practical implications The approach provides a computationally tractable way to discover interpretable dispatching rules for dynamic manufacturing environments with uncertain processing times and limited historical data. By reaching strong rules earlier, MGAFGP can reduce the simulation budget needed for rule evolution, support managerial inspection of scheduling logic and reduce reliance on expert-designed heuristics. Originality/value The study integrates generalized grey-number processing times into the DFJSP and develops a GP algorithm with separate feature probability adaptation for routing and sequencing. The elite-guided strategy with generation-dependent parent selection provides a mechanism for accelerating convergence in simulation-based GP under grey processing-time uncertainty.
Purpose In the era of big data, the understanding of the complex and uncertain nature of reliability growth data has deepened. Beyond the well-known characteristic that failure data are random variables following specific probability distributions, expert judgments expressed linguistically constitute fuzzy data. Allowable values for critical parameters are often confined to specific ranges, representing typical grey data. Moreover, knowledge regarding specific components, materials and processes frequently manifests as rough data. Effectively utilizing reliability growth data characterized by multiple uncertainties – randomness, fuzziness, greyness and roughness – is therefore key to solving the modeling challenges for reliability growth of high-end intelligent equipment. This paper proposes a novel model and associated new concepts for uncertainty representation and integration to address this gap. Design/methodology/approach Guided by the core principles of big data – which emphasize utilizing all available data beyond random sampling, eliminating confounding factors to discern general trends and prioritizing correlation over strict causality – this research adopts a “full data utilization” perspective. It begins with the collection, identification, and analysis of reliability growth data. Through an in-depth examination of the characteristics and commonalities of data embodying various uncertainties (random, fuzzy, grey and rough), the concept of a standard uncertainty number is defined. The representation of SUNs, conversion rules for transforming diverse uncertainty data into SUNs and a comprehensive operational framework for SUNs are developed. Subsequently, analytical and data mining models based on SUNs are established. These models facilitate multi-dimensional, multi-stage and multi-level exploration of key factors influencing the reliability growth of high-end intelligent equipment, leading to the construction of a reliability growth evaluation index system. To overcome existing modeling bottlenecks, holographic reliability growth evaluation and prediction models are constructed by integrating big data technologies, complex uncertainty data analysis methods, sequence operators, spectrum analysis and intelligent algorithms. Findings The proposed novel concepts and framework demonstrate the feasibility of integrating diverse uncertainties to achieve high reliability for complex equipment. Research limitations/implications The limitation of this research is its coverage of various uncertainties. It is not possible to cover fully all uncertainties due to their unknown status, and the proposed model provides only a method rather than a completed solution to the challenge. Practical implications Manufacturers employ reliability growth tests to iteratively enhance equipment reliability and performance through cycles of “exposing defects – analyzing causes – implementing improvements.” However, when data fail to meet the assumptions of traditional reliability growth models, practitioners often resort to ad hoc measures – such as using simulated data or borrowing data from similar equipment – which may compromise reliability. Traditional models constrained by random sampling are evidently inadequate for the development of complex equipment, necessitating new approaches. The concepts and models proposed in this paper have the potential to significantly improve the quality and reliability of complex products in smart manufacturing. Originality/value While numerous uncertainty models exist, effective frameworks for their integration remain scarce. The definitions, operational systems of SUNs, the various SUN-based data mining models and the holographic reliability growth evaluation and prediction models presented here are original contributions of the authors.
Purpose In order to enhance the prediction accuracy of the grey model in small-sample, high-volatility scenarios and to effectively utilize spatial effects and data autocorrelation features, a weighted grey Markov forecasting model with spatial effects is constructed. Design/methodology/approach A spatial effect module is incorporated to capture inter-regional correlations and heterogeneity, and a weighted Markov chain module is introduced, which adjusts the weights of different state transition steps to better utilize recent data. Findings Experimental results on talent and electricity demand data from multiple regions show that the proposed model significantly outperforms baseline models in prediction accuracy, and ablation studies validate the effectiveness of both the spatial effect module and the weighted Markov chain module. Originality/value Integrating spatial effects into the grey model and leveraging a weighted Markov chain to fully account for the autocorrelation characteristics of the data series, the proposed approach enhances both adaptability and predictive performance in highly volatile scenarios.
Purpose To improve emergency-demand prediction under small-sample, high-volatility conditions, this study proposes a conformable quantum Simpson fractional grey model (CQSFGM). Design/methodology/approach The CQSFGM models fractional memory through conformable fractional accumulation (CFA) and conformable fractional difference (CFD), reconstructs background values using Simpson rule discretization to reduce truncation error compared with the trapezoidal rule, optimizes the fractional order via quantum-behaved particle swarm optimization (QPSO) to avoid subjective tuning, and updates the data in combination with the metabolic mechanism to adapt to non-stationary emergency demand data. Findings In the practical case, the mean absolute percentage error (MAPE) of CQSFGM is consistently lower than that of other benchmark models. Furthermore, robustness analyses confirm that this predictive advantage remains statistically significant under varying small-sample sizes and high-intensity noise perturbations, thereby providing support for emergency supply. Originality/value The CQSFGM model improves both accuracy and adaptability for emergency demand prediction.
Purpose This paper constructs a grey matrix correlation model to thoroughly investigate the integration mechanism between the digital and manufacturing industries and to objectively evaluate their correlation within the Yellow River Basin.Design/methodology/approach First, based on spatial geometry and calculus theory, the surface representation method of behavioral matrices in three-dimensional space is explained, and the calculation method for the volume of the corresponding surface body is provided. Second, inspired by the two-dimensional grey absolute correlation model, a grey matrix correlation model based on the volume of the surface body is established. We analyze the properties of the proposed model, including normalization, proximity, and order preservation under scalar multiplication. Additionally, the MATLAB implementation code for the model is provided to enhance its operability. Finally, the model is applied to empirically analyze the correlation between manufacturing and the digital industry in the Yellow River Basin.Findings The results validate the effectiveness and rationality of the model, and policy recommendations are proposed to optimize resource allocation and enhance the digitalization level of manufacturing in the region.Originality/value This study provides a theoretical basis and methodological support for promoting the high-quality development of manufacturing in the Yellow River Basin, while also offering insights for other regions exploring pathways for the integration of the two industries.
Purpose To address the numerical discretization errors caused by singular kernels and the overfitting risks associated with generalized operators in existing fractional grey models, this paper proposes a theoretically rigorous Generalized Conformable Fractional Grey Forecasting Model, GCFGM(1.1).Design/methodology/approach The model is established based on the right-fractional rectangular formula to ensure mathematical consistency between the continuous integral and discrete accumulation. The inverse restoration is implemented via matrix inversion to eliminate recursive errors. Furthermore, a constrained particle swarm optimization (PSO) algorithm with a regularization mechanism is designed to optimize the fractional order alpha and accumulation order r. This strategy mathematically constrains the solution space to balance fitting accuracy with model complexity.Findings Empirical validation is conducted across three datasets representing distinct dynamic patterns: stable exponential growth (R-GDP), saturation trends (Researchers per million inhabitants (FTE)) and irregular volatility (education expenditure). Results demonstrate that GCFGM(1,1) significantly outperforms classic integer-order and fractional models.Originality/value This study bridges the gap between continuous generalized operators and discrete time series modeling. It contributes a rigorous numerical framework that resolves the singularity issue and introduces a regularization strategy to mitigate the ill-posedness problem in small-sample forecasting.
PurposeTo enhance the forecasting accuracy and robustness of photovoltaic (PV) power generation, this study proposes a fluctuating shape-adapted seasonal grey prediction model that effectively captures seasonal variation and time-varying amplitude in PV data.Design/methodology/approachFirst, a fluctuating shape-adapted seasonal term is designed in the SGMFSA(1,1) model to adjust periodic parameters. Then, the WOA algorithm is utilized to solve for nonlinear parameters, facilitating the accurate identification of optimal estimates within the proposed model. Moreover, the SGMFSA(1,1) model's performance is evaluated on two real-world PV datasets (quarterly and monthly), benchmarked against two statistical models, four machine learning algorithms, and five grey models.FindingsEmpirical results show that the SGMFSA(1,1) model consistently outperforms all benchmark models in terms of forecasting accuracy and stability. In Cases 1 and 2, SGMFSA(1,1) achieves average MAPE of 1.8 and 4.2%, reducing errors by 82.5 and 52.8% compared to benchmark models, with APE ranges narrowed by 88.7 and 65.9%, respectively, demonstrating superior accuracy and stability. Probability density analysis further confirms the model's superior robustness.Practical implicationsThe proposed model provides an effective forecasting framework for PV power generation, which is critical for improving grid stability, optimizing energy scheduling, and supporting policy and investment decisions in the renewable energy sector.Originality/valueConsidering the limitations of existing forecasting models in handling PV data with volatility and time-varying amplitudes, we design a novel fluctuating shape-adapted seasonal grey prediction model (SGMFSA(1,1)) to address the time-varying volatility of photovoltaic power generation data.
PurposeWhen using the grey possibility clustering (GPC) model, the possibility function is usually constructed based on the subjective judgment of decision-makers (DMs). Despite existing approaches of the inverse grey possibility clustering (IGPC) are put forward to construct the possibility function in a quantitative way, computational procedures are complicated. Consequently, this study proposes a grey possibility clustering optimization model (GPCOM) which can generate a possibility function that minimizes the greyness of clustering outcomes based on part of the given clustering results by solving the proposed nonlinear programming model.Design/methodology/approachFirstly, based on the unified expression of the center-point mixed possibility function (CMPF) and the matrix expression of the clustering coefficient, constraints of GPCOM under four scenarios are constructed. Subsequently, aiming to maximize the differences among clustering coefficients, four GPCOMs are put forward and corresponding solution algorithms based on the whale optimization algorithm (WOA) are proposed. Finally, the proposed model is applied to a case study.FindingsEmpirical results reveal that, compared with the forward GPC model, the proposed GPCOM and its algorithm achieve markedly higher clustering accuracy while offering a significantly simplified computational procedure.Originality/valueThe GPCOM proposed in this paper can be employed to derive the most feasible possibility functions that satisfy the given known clustering results but also can minimize the greyness of clustering results by maximizing the disparity of the clustering coefficients. It represents a novel greyness-minimization principle in inverse grey clustering theory.
PurposeMulti-Attribute Decision-Making (MADM) methods often yield inconsistent rankings of alternatives due to their distinct computational mechanisms, complicating the selection of optimal solutions. This study proposes a novel grey-based aggregation framework to systematically resolve such inconsistencies.Design/methodology/approachThe framework employs Grey Systems Theory to quantify ranking uncertainties through interval grey numbers. A Python-coded algorithm compares these grey numbers using possibility degree functions, enabling systematic aggregation of divergent rankings. The approach is demonstrated through a supplier selection case study combining results from nine MADM techniques.FindingsThe framework effectively resolves ranking conflicts while preserving the strengths of individual MADM methods. Computational results validate its ability to produce stable, consensus rankings from inconsistent inputs.Practical implicationsOrganizations can apply this approach to integrate diverse MADM recommendations in complex decisions like sustainability assessment, supply chain management, resource allocation, healthcare systems or performance evaluation, particularly where methods disagree.Originality/valueWhile MADM methods each offer unique advantages in handling specific decision scenarios, their inconsistent outcomes create practical challenges. This research provides a GST-based solution that computationally reconciles these differences through grey number comparison, implemented via Python for practical application.
PurposeAccurate prediction of energy consumption is essential to provide data reference for policy makers in energy-related sectors, while existence of mixed patterns, including linear, nonlinear and time-varying effects, makes its prediction complicated. To effectively capture dynamics in time series, a novel mixed effects-based multivariate gray model is proposed to improve the prediction performance.Design/methodology/approachFirst, the nonlinear and time-effect terms are introduced into the typical multivariate gray model with convolution integral, which aims to simultaneously capture mixed dynamics in diverse sequences. Second, the gray wolf optimizer (GWO) algorithm is applied to identify the optimal model parameters. Additionally, a Monte-Carlo simulation is conducted to assess the computational efficacy and prediction performance of the novel model combined with GWO.FindingsThree real-world cases, namely energy consumption data from three countries, are utilized to evaluate the robustness and reliability of the novel model compared with others. The numerical results show that the novel model enables the identification of the mixed dynamics of energy consumption systems and then enhances the accuracy performance in forecasting energy consumption.Originality/valueA novel mixed effects-based multivariate gray model is introduced, which is supported by rigorous mathematical proofs of its properties. Additionally, three case studies compare this model with eight other benchmark models.
Purpose This study tackles two challenges in aluminum-magnesium (Al-Mg) alloy rolling – control delay from measurement hysteresis and strong nonlinearity with limited passband precision – by proposing a predictive control scheme that couples an optimized starting-point combinatorial discrete grey model (OSCDGM), with an improved PID neural network (IPIDNN). Design/methodology/approach An OSCDGM framework based on an Optimized Starting-Point Discrete Grey Model (OSDGM) uses change-point-driven updating with tail correction and Fourier-series residual compensation to achieve high-accuracy real-time prediction of inter-stand thickness. Predicted and measured values are fused to drive online learning of an IPIDNN controller, which augments a PID neural network through variable-speed integration, incomplete differentiation and tanh-based nonlinear mapping to enhance tracking, passband control and dynamic response. Findings Field experiments show that OSCDGM reduces prediction errors by 36–42% relative to Even Grey Model (EGM), Discrete Grey Model (DGM) and Support Vector Machine (SVM). IPIDNN shortens settling time by 79–88% compared with Back Propagation-Proportional-Integral-Derivative (BP-PID), PID Neural Network (PIDNN) and model predictive control. Under disturbances and noise, the standard deviation of control deviation is reduced by 68% versus conventional PID, with fluctuations confined within ±3s and thickness accuracy improved by about 27% in production. Research limitations/implications Application to full-pass rolling of AZ31B alloy verifies engineering applicability and demonstrates markedly improved thickness consistency and stability, while highlighting the need to assess generalization to alloys with different plastic properties. Originality/value The study establishes an integrated architecture combining high-precision dynamic prediction with structurally enhanced neural-network-based control, providing a paradigm for intelligent control of high-precision metal rolling with significant time delays and nonlinearity.
Purpose This study addresses a dual-resource constrained flexible job shop scheduling problem (DRCFJSP) in the context of Industry 5.0, where both machines and workers must be coordinated. It incorporates a team-based collaborative learning effect that dynamically enhances worker proficiencies and uses interval grey numbers to represent uncertain processing times. The aim is to optimize makespan, maximum team workload, and total worker proficiency improvement simultaneously. Design/methodology/approach A multi-objective grey dual-resource constrained flexible job shop model is proposed, integrating interval grey numbers to represent uncertainties and a collaborative learning effect to reflect skill evolution. To solve this problem, a knowledge-guided multi-objective evolutionary algorithm (KGMOEA) is designed, featuring a four-layer encoding scheme and domain-specific strategies such as knowledge-guided population initialization and neighborhood search. Findings The proposed algorithm outperforms benchmark methods in convergence and diversity. Incorporating collaborative learning effects reduces total completion time and improves resource allocation efficiency. Experimental results confirm that the method effectively balances production efficiency with workforce skill development under uncertainty. Practical implications This paper provides a practical scheduling framework for high-complexity manufacturing environments, such as aviation composite workshops, where human–machine collaboration and skill development are critical. The proposed approach helps to optimize both production efficiency and worker proficiency growth under uncertain conditions, supporting resilient and sustainable manufacturing in the industry 5.0 era. Originality/value This paper is the first work to integrate collaborative learning effects and interval grey numbers into the DRCFJSP, addressing both dynamic skill evolution and production uncertainties simultaneously. The work contributes to the shift from machine-centered to human–machine collaborative scheduling and provides a new model and algorithm for learning-oriented scheduling in uncertain environments.
Purpose Accurate energy data prediction holds significant practical importance for optimizing energy structures and informing governmental energy decision making. Due to the uncertainty inherent in energy sequences, this paper proposes a hybrid model combining seasonal–trend decomposition and a nonlinear time-delay grey model. Design/methodology/approach The trend variations inherent in the data are obtained through signal decomposition techniques, and higher weights are assigned to new information within the model. Prediction results are restored via seasonal factors, and the optimal parameter values are obtained using the PSO algorithm. Findings An analysis of the model’s various characteristics is conducted. By fitting and forecasting China’s natural gas production data and comparing the results with those of four other benchmark models, the validity of the model is verified. Originality/value This study extends trend decomposition and seasonal factor restoration by incorporating nonlinear terms, lagged terms and new information priority, enabling the model to better adapt to dynamic trend changes and significantly improve prediction accuracy for time series with prominent dynamic trends and seasonal variations.
PurposeThe study aims to identify sustainable packaging solutions in the automotive logistics industry by assessing their economic, technical and environmental performance. It aims at finding packaging alternatives that meet the needs of key stakeholders with a focus on the circular economy in the automotive supply chain.Design/methodology/approachThe study proposes a novel beta-transformative grey incidence analysis (BTGIA) model by integrating Javed's framework for dynamic distinguishing coefficients and beta transformations of the coefficients. Data were collected from three groups of experts, representing the interests of automotive manufacturers, packaging technology experts and sustainability and regulatory professionals.FindingsReturnable and collapsible containers and reusable plastic crates were identified as the best solutions owing to the fact that they are both reusable and efficient. Biodegradable packaging was important for regulatory professionals but was less important for the manufacturers, indicating the divergence of interests. The priorities of stakeholders differed considerably, with manufacturers focusing on cost and sustainability and regulatory professionals focusing on the circular economy.Originality/valueThe paper presents a new model of sustainable packaging assessment called the BTGIA, advancing a methodological innovation in grey multi-criteria decision-making. It offers practical insights into the divergence of interests among different stakeholders and their differing priorities.
PurposeAccurate forecasting of Europe's battery electric vehicle (BEV) market is crucial for trend analysis and policy formulation. This study aims to propose an innovative discrete grey model specifically designed for predicting BEV sales in Europe.Design/methodology/approachThis study innovatively integrates fractional-order accumulated (FOA) with an enhanced driving term that incorporates integer-order polynomials and time-dependent power terms, thereby developing an optimized discrete grey prediction model. The particle swarm optimization algorithm (PSO algorithm) was employed for parameter optimization, and solution stability was thoroughly investigated. Through comparative analysis with three benchmark models using real-case studies, the effectiveness and forecasting accuracy of the proposed model were validated, followed by its application to predict future BEV sales in Europe.FindingsThe proposed model demonstrates effective applicability for BEV sales forecasting. In the coming years, European BEV sales are projected to exhibit a stable growth trend.Practical implicationsThe proposed model can be effectively applied to forecast and analyze both BEV sales volume and market prospects in Europe. Based on the forecasting and analytical results, corresponding policy recommendations are provided.Originality/valueThis study pioneers a FOA discrete grey polynomial model that incorporates time-power terms, representing a novel grey prediction model with superior performance characteristics.
PurposeThe purpose of this paper is to show Industry 4.0 technologies the potential of Industry 4.0 technologies to reduce the environmental impact of manufacturing processes and transform business models towards sustainability. In this study, the ERP selection process is examined with sustainability and Industry 4.0 criteria under fuzzy and grey uncertainty methodologies. Design/methodology/approachA case study employed the intuitionistic fuzzy sets-based grey ordinal priority approach (OPA-G) methodology to evaluate sustainability criteria that are in line with the 17 Sustainable Development Goals (SDGs) by the United Nations and seven generic framework applications of Industry 4.0 compatibility. This approach was particularly chosen to address the uncertainties involved in selecting appropriate and reliable ERP software. FindingsIn this study, the enterprises often prioritize economic performance over environmental and social criteria. However, there is also recognition of the importance of integrating Industry 4.0 technologies such as cloud and edge computing, artificial intelligence, the Internet of Things, and big data in ERP selection processes to foster sustainable practices. Practical implicationsIndustry 4.0 technologies enhance sustainability by providing real-time data analytics, increasing supply chain transparency, and optimizing resources to minimize waste and environmental impact. These innovations help businesses align with global sustainability standards, balancing economic, environmental, and social goals considering the circular economy (CE) while appealing to conscious consumers and investors. Originality/valueThis study introduces a novel use of the intuitionistic fuzzy set-based grey OPA methodology to evaluate sustainability criteria in ERP software selection, focusing on incorporating sustainability uncertainties and highlighting the importance of Industry 4.0 technologies for sustainable development under CE.
Purpose- This study aims to construct a new grey model to assess the COVID-19's impact on China's domestic tourism revenue. Design/methodology/approach- Firstly, the Hausdorff accumulative generation operator and adaptive nonlinear correction term are introduced to the new model, with parameter optimization using PSO. Then, the new model is applied to assess the epidemic's impact on China's domestic tourism revenue. Findings- The performance result of the Hausdorff accumulative generation operator and adaptive nonlinear correction show that they can improve the model's prediction stability and simulation accuracy. The model result shows from 2020 to 2022 the average contribution of the epidemic to revenue is -64.51%, with a loss of 132,027.6 million yuan. Originality/value- This study has positive implications for enriching the application method of grey prediction model.
