Accurate Air Quality Index (AQI) forecasting is essential for public health protection and sustainable urban planning. Existing data-driven forecasting models often provide limited interpretability of pollutant interactions, while conventional Fuzzy Cognitive Map (FCM) learning algorithms may struggle to optimize causal weights effectively. To address these limitations, this study proposes IGWO-FCM, an evolutionary-cognitive framework that integrates an Improved Grey Wolf Optimizer (IGWO) with FCMs for interpretable causal structure learning and AQI forecasting under uncertainty. The framework employs FCMs to represent pollutant interactions and feedback mechanisms, and introduces a hierarchical transformation operator and adaptive learning strategy to enhance causal weight optimization. On a real-world urban AQI dataset comprising 744 hourly records and six pollutants, as well as two public benchmarks, IGWO-FCM achieves the lowest MAE and RMSE among the compared FCM learning algorithms for five of the six pollutants, reducing these errors by up to 29.6% and 40.2%, respectively, relative to the strongest baseline. These results demonstrate the predictive performance of IGWO-FCM and its potential to provide interpretable insights into pollutant interactions for AQI forecasting.

The failure mode and effect analysis (FMEA), as an effective proactive reliability analysis technique, plays an important role in system fault detection and reliability maintenance due to its pre-analysis capability. Although traditional FMEA is widely used in practice, it has some limitations in the expression of fuzzy information, considering the interrelationships between risk factors, and considering relative importance. Therefore, a new FMEA method that combines spherical fuzzy set (SFS) and an improved spherical fuzzy weighted Hamy mean (SFWHM) operator is proposed. This method mainly includes four stages. Firstly, the SFS is applied to obtain risk assessment information, as it can handle more ambiguous information. Secondly, to ensure that the quality of evaluation information meets specific standards, consensus calculation and feedback mechanisms are introduced. Next, risk factor weights are obtained based on the logarithmic percentage change-driven objective weighting (LOPCOW) method and an improved spherical fuzzy score function. Finally, based on the proposed SFWHM operator, the risk factor information with interrelationships is integrated, and an improved score function is used to obtain the final ranking results. The proposed method is applied to the load-bearing guidance device of the subway door system to verify its applicability and compare its advantages with existing advanced FMEA methods. The results indicate that the proposed method provides a reliable tool for practical FMEA problems. The proposed method, as a reliable risk assessment technique, can be flexibly applied to various practical scenarios.