Accurate forecasting of urban domestic waste clearance in China is essential for advancing the sustainable development of urbanization. To this end, this paper proposes a novel nonlinear grey convolution model that incorporates background value optimization. Firstly, this model introduces power exponents to enhance its ability to capture the nonlinear characteristics of the system. And then, it also analyzes the sources of errors in the background value calculation of traditional models and effectively addresses this issue by incorporating dynamic interpolation coefficients. Besides, the optimal hyperparameters of the model are determined using particle swarm optimization (PSO). In two distinct case studies, the proposed model was rigorously compared with five forecasting models across three distinct domains, consistently demonstrating its superior performance.

The grey Bass model serves as a valuable tool in forecasting time series portraying inverted U-shaped characteristics. However, the existing grey Bass model still has some issues in inaccuracies for the Cusum operator and the rationale behind selecting the initial value for parameter estimation. To improve the accuracy and applicability of the grey Bass model, the generalized grey Bass model is developed, incorporating the physics-preserving Cusum operator with second-order accuracy. Initially, the relationship between the generalized grey Bass and the traditional grey Bass models is elucidated via parameter transformation. Subsequently, opting for the first observation as the initial value is proven to be not only accurate but also a highly efficient strategy. Additionally, extensive simulations are conducted to compare both models in terms of robustness against discretization errors, measurement noise, and sample size. Finally, the generalized grey Bass model is applied to two real-world cases and evaluated against competitive models regarding accuracy and stability. Results demonstrate that the generalized grey Bass model exhibits superior precision and exceptional modeling performance.

To tackle the challenges of inventory models in practical applications, this paper introduces a grey forecasting modeling approach to uncover the inventory differential equation and subsequently develops an inventory optimization model. Firstly, for deteriorating products with price-dependent demand, this article formulates a differential equation to describe inventory levels by analyzing the inventory system and develops an optimization model aimed at maximizing inventory profits. Based on the idea of grey forecasting modeling, this article discusses the problem description of identifying the inventory differential equation. Then, by using the cumulative generation operator, the parameter estimation of the inventory differential equation is transformed into a regression problem. A numerical example is presented to illustrate the steps of grey forecasting modeling. The simulation results validate the feasibility of the grey forecasting modeling in the simulation case.

Macroeconomic indicators offer critical insights into the economic performance of nations. The potential variability of these factors necessitates formulating policies and implementing actions to counteract any adverse situations that may arise. This research aims to evaluate the macroeconomic performances of the seven developed nations, known as the G7 nations. The research identified imports of goods and services, exports of goods and services, gross fixed capital formation, gross domestic savings, unemployment, population, current account balance, inflation, consumer prices gross domestic product as criteria for performance assessment. An integrated framework integrating the LOPCOW-G and RAWEC-G methodologies is presented to assess the macroeconomic performance of G7 nations within the study's framework. The weight values derived from the LOPCOW-G technique indicate that the current account balance is the most significant factor influencing macroeconomic success. The RAWEC-G technique findings indicate that Japan had the highest economic performance, while the USA demonstrated the lowest economic performance.

The rapid development of the economy in Xinjiang has brought about an increased emphasis on the coordination between the major layout and the industrial structure of Xinjiang higher vocational colleges. This study investigates the correlation between the major layouts of these institutions and the regional industrial structure through the use of an integrated grey system framework. The employment of grey correlation modeling (ρ=0.5) and a particle swarm-optimized fractional grey prediction model (FGM(1,1) with r=0.75) has led to the following three key findings: Firstly, the overall major layout of higher vocational colleges in Xinjiang is largely consistent with the current industrial structure demand. Secondly, it will be necessary to strengthen the construction of majors related to emerging industries and modern service industries to adapt to changes in the industrial structure. Thirdly, the findings prove that the fractional-order grey prediction model is an advanced scientific approach to adapt the major layout to regional industries, which provides a better tool in serving local economic and social development. These findings validate the efficacy of fractional grey models in the realm of vocational education planning, offering a replicable framework for the management of industrial transition in developing regions.

This paper introduces an advanced EEG-GRA cross-sequence feature extraction method for operator cognitive fatigue detection in industrial settings. Our research addresses key limitations in conventional approaches through three technical innovations: (1) an intelligent adaptive time-varying weight function system that continuously calibrates to operator cognitive states, (2) an advanced multi-scale analysis framework incorporating state-of-the-art wavelet decomposition, and (3) a sophisticated cross-sequence feature fusion mechanism that leverages spatial correlations across EEG channels. Comprehensive performance evaluation reveals significant quantifiable improvements: the system achieves a 45% reduction in processing time (from 100ms to 55ms), enabling genuine real-time monitoring capabilities; detection accuracy shows a remarkable increase of 17.5 percentage points (from 76% to 93.5%); and signal quality demonstrates a substantial improvement of 5.3dB (from 15dB to 20.3dB). These advances are achieved while simultaneously reducing computational demands, with algorithmic optimization decreasing complexity from O(n²) to O(n log n) and memory requirements reduced by 38%. Field implementation in a nuclear power plant control room involving 30 operators under rigorous operational conditions validated the system's exceptional reliability, maintaining 99.99% uptime during 12-hour continuous monitoring shifts. Statistical analysis confirms the significance of these improvements (p < 0.01), establishing a new benchmark for industrial safety systems across high-risk sectors.

In the digital age, the rapid dissemination of false information on social networks presents certain societal challenges. Traditional detection methods have some limitations in handling data uncertainty and incompleteness common in social media environments. Therefore, this study proposes a grey relational clustering model, tentatively integrating content features, user behaviors, and propagation network features to better address data uncertainty and incompleteness. Preliminary comparative experiments with conventional machine learning and deep learning approaches indicate that our model maintains accuracy above 85% even when 30% of data is missing, and achieves an accuracy of 92% and an F1-score of 0.92 on complete datasets. Additionally, the model demonstrates certain advantages in computational efficiency, being approximately 2.5 times faster than traditional machine learning models and about 9 times faster than BERT. This research hopes to contribute modestly to real-time false information detection by providing a relatively efficient and somewhat adaptive analytical tool for social media environments.