In order to enhance the precisions of grey prediction models, it is essential to address the univariate constraints of the traditional GM(1,1) model and consider the influences of data’s time delay and nonlinear mapping on system behavior. In this paper, based on the grey model with background value optimization, we propose a time-delay optimized grey BP neural network combinatorial model (BP-TDOGM(1,1)) by introducing a time-delay causal term and combining with the BP neural network. The mechanisms of time delay, nonlinear mapping and related factor sequences on system behaviour are discussed in detail. Furthermore, the modelling framework, parameter estimation methods and model resolution techniques are investigated with a view to enhancing the capture of data correlations. These endeavours are designed to extend the scope of application of neural networks in scenarios characterized by limited information and to markedly optimize the prediction accuracy of the grey forecast model. Ultimately, the proposed model's efficacy is validated through an example of forecasting China's power production. This example offers a novel approach to address the practical challenges posed by limited time-delay information. It also serves as a decision-making reference for China's power sector, ensuring the harmonious development of power supply and the economy.

The traditional energy phase-out and new energy substitution are critical to achieving the dual-carbon goal. Effectively coordinating these processes is essential for ensuring China’s energy security and achieving long-term carbon reduction. First, a Multi-Level Perspective (MLP) analysis framework is developed to examine the process of the traditional energy phase-out and new energy substitution under the dual-carbon goal, focusing on the misalignment mechanisms and their types. Second, an indicator system for evaluating misalignment risks is established, incorporating four key dimensions: new energy substitution capacity, new energy substitution level, traditional energy phase-out level, and carbon emission reduction achievement. Furthermore, a time-series cobweb grey target model is developed to evaluate and forecast misalignment risks during China’s 14th and 15th Five-Year Plan periods, and risk identification criteria are proposed. Empirical results confirm the effectiveness of the time-series cobweb grey target model.

Combat effectiveness assessment plays a crucial role in modern military operations, and its effectiveness directly affects combat

efficiency, resource allocation and decision support. Firstly, the phase angle in quantum interference theory is introduced as the

interference adjustment factor of grey correlation model, in which the traditional combat indicator system is reconstructed and

optimized. Secondly, the properties and theorems of the grey correlation model after the introduction of quantum interference are

analysed, and based on the quantum entanglement characteristics of UAV combat, its combat effectiveness is quantitatively evaluated through the quantum interference-grey correlation model. Finally, the effectiveness of this study is illustrated by a case study of UAV cluster formation programme. The results of the study show that the index assessment method not only improves the accuracy of combat effectiveness assessment, but also provides powerful support for actual military decision-making, demonstrating a wide range of application potential and important practical value.

Aiming at the interference problem between decision-makers in uncertain group decision making, this paper proposes a new interference angle measure method based on quantum-like Bayesian network (QLBN). Firstly, the grey relational degree is extended to the positive and negative range, and then the grey relational degree is calculated according to the sequential growth trend, and it is transformed into the interference value. In this framework, the weights of the decision-makers are set as the first layer of QLBN, where they are determined based on the similarity between the personal opinion and the leading decision-maker’s opinion, and the conditional probabilities are calculated by combining the attributes’ weights and evaluation values. Finally, the quantum probabilities of alternatives are obtained. The alternatives are ranked according to the quantum probabilities, and the robustness and validity of the model are verified by numerical example. The result shows that the interference angle calculation method based on grey relational degree has a good performance in decision-making scenarios with incomplete information, and significantly improves the robustness and applicability of the quantum decision model.

The evaluation of large aircraft suppliers' importance is crucial for supplier management and project stability. A method combining grey clustering and complex network theory is proposed for evaluating the importance of aircraft suppliers. The collaborative development network for the aircraft is first constructed through the work breakdown structure. Four centrality indicators of supplier network nodes are then employed, and a grey clustering model based on center-point mixed possibility function is applied to classify the suppliers. Taking the C919 aircraft as a case study, 43 suppliers are categorized into three levels. The roles and

relationships of suppliers at each level within the collaborative development network are analyzed. The effectiveness of the evaluation model is verified, providing management insights and strategic recommendations for optimizing supplier management for the aircraft manufacturer

In order to solve the pattern recognition problem that the index value and weight are both interval grey numbers, a multi-index grey pattern recognition model based on generalized greyness is established in this paper. Firstly, the basic concepts of grey pattern, universal grey pattern and grey pattern recognition are given, and the principle of maximum possibility degree and the possibility function of single index grey pattern are given. Secondly, two methods of multi-index grey pattern recognition are given, that is, the comprehensive possibility degree model and proximity degree model, and the simplified forms of proximity degree model are given. Finally, the grey pattern recognition model is applied to the high-quality development evaluation of 15 national agricultural science and technology parks in Shandong province of China to verify the validity of the model. The results show that the proposed grey pattern recognition model has the advantages of strict mathematical foundation, clear physical meaning, simple calculation and easy programming. The application examples show that the proposed grey pattern recognition model is feasible and effective. The research results not only enrich the theory of grey mathematics and grey system, but also provide a new way for grey pattern recognition in cases where the weights and index values are all interval grey numbers or the coexistence of interval grey number and real number.

The conformable fractional accumulation generating operator (CF-AGO) can effectively handle information differences and deeply

explore the laws of information development. Nevertheless, the CF-AGO fails to satisfy the highly crucial new information priority

(NIP) principle. In this paper, a novel conformable fractional accumulation generating operator (NCF-AGO), which meets the NIP

principle under certain conditions, is introduced firstly. Then an improved conformable fractional grey multivariate model with

variable NCF-AGO is constructed. Both linear and nonlinear correction terms are considered in the model structure to fit data

sequences with different features. The quantum particle swarm optimization algorithm is adopted to obtain the optimal accumulation

orders and the optimal power exponent of the nonlinear correction term. In order to avoid the situation where overfitting of the model leads to poor prediction results, the Tikhonov regularization method, which includes the conventional least squares method as a special case, is proposed solve the involved model parameters. Finally, a case study from bending strength of concrete is given to show the effectiveness of the proposed model and its advantages over the well-known GM(1,N) model and several existing grey multivariate models.

With the advancement of educational informatization and personalized learning, scientific evaluation of learning outcomes has become crucial for educational quality assurance. This paper proposes a hybrid evaluation approach integrating grey correlation analysis, BP neural network, and fuzzy evaluation based on EEG data for assessing personalized learning effects. The method establishes objective evaluation indicators through EEG data analysis, enabling real-time monitoring and assessment of the learning process. By adopting a multi-model fusion strategy, the accuracy and reliability of the evaluation are enhanced. The evaluation framework encompasses data preprocessing, feature extraction, model fusion, and result validation. Empirical research in primary education demonstrates that this method achieves 89% consistency with expert evaluation, 85% accuracy in cross-validation, and a correlation coefficient of 0.82 with academic performance. Over an eight-week intervention period, students showed significant improvements: attention levels increased by 35%, learning efficiency improved by 40%, and assignment quality enhanced by 28%. The research findings provide a new paradigm for data-driven educational evaluation and make significant contributions to advancing scientific and personalized development in educational assessment.

Providing eHealth services to elderly individuals with disabilities has become a critical global issue, especially in Pakistan, where

access to these services often presents significant barriers that need to be identified and explored to ensure equitable and effective

healthcare delivery. Therefore, this study aimed to identify and rank the barriers to access eHealth services for Pakistani disabled

elderly. A survey was conducted to collect primary data, and 322 elderly people with disabilities provided their consent about facing

barriers to eHealth services. The questionnaire was based on technological, individual, relational, environmental, and organizational constructs. Multiple-criteria Decision-making (MCDM)-based Dynamic Grey Relational Analysis (DGRA) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) were applied to explore and rank the significant barriers. We found the barrier “fear and dislike of technology” to be the top-ranked barrier evaluated from both DGRA and TOPSIS techniques. The Kruskal-Wallis (KW) test was also performed to assess the significance of this barrier for the three age groups of disabled elderly and found no significant differences among their age groups when aged ≥ 60 years. In Pakistan, this study is the first to use the DGRA, TOPSIS, and KW tests to examine the rank and significance of barriers to access eHealth services for the disabled elderly.

To address the issues of nonlinearity, time-varying characteristics and new information priority in processing complex data, this paper proposes a new information priority adaptive nonlinear grey Bernoulli model. By integrating the Bernoulli equation, the time power term and the new information priority accumulation operator, the proposed model fully utilizes the effective information within sparse sample, thereby enhancing the adaptability of grey prediction models to nonlinear and volatile time series. This model's hyperparameters are solved using the Particle Swarm Optimization algorithm, and the objective function is optimized. Meanwhile, a quantitative method is adopted to select the modeling sequence of the case study. In the prediction of China's high-tech industry output, the new model is compared with five benchmark models and subjected to robustness testing. The results indicate that the new model outperforms the comparison models in terms of prediction performance, and exhibits strong robustness. Furthermore, the future output value of China's high-tech industry is predicted.