Performance of five methods under Laplace noise.

The evolving patterns of pollutant concentrations and their rigorous assessment are critical issues in contemporary environmental research and policy-making, with important practical implications for air quality management and regional pollution control. To better support such decisions, scientifically sound multi-criteria ranking methods have become a key research focus. In this paper, we propose a novel adaptive functional piecewise ordered weighted averaging (FP-OWA) method for ranking complex functional data. The method extends the existing functional piecewise ranking–weighting framework by integrating data smoothing, depth-based centrality measures, and rank-based aggregation. We systematically compare the performance of FP-OWA with several existing functional data ranking methods using Monte Carlo simulations. The results show that FP-OWA substantially improves ranking consistency and stability when the data are contaminated by white noise. We further apply FP-OWA to rank the daily average PM2.5 and O3 concentrations in 13 cities in the Beijing–Tianjin–Hebei region in 2023, accurately revealing the spatiotemporal differentiation patterns of regional pollution. These findings provide a solid technical basis for local governments to design pollution control strategies and improve air quality. Future research will focus on extending FP-OWA to highly nonlinear and complex functional data, further enhancing its computational efficiency to meet big-data processing requirements, and exploring additional application scenarios.污染物浓度的演化特征及其严谨评估是当代环境研究与政策制定中的核心议题，对空气质量管控与区域污染防治具有重要的现实意义。为更好地支撑此类决策，科学合理的多准则排序方法已成为重要的研究热点。本文提出一种全新的自适应泛函分段有序加权平均（adaptive Functional Piecewise Ordered Weighted Averaging，FP-OWA）方法，用于复杂泛函数据的排序任务。该方法在现有泛函分段排序-加权框架的基础上，整合了数据平滑、基于深度的中心性测度与基于秩的聚合方法。本文通过蒙特卡洛（Monte Carlo）模拟，系统对比了FP-OWA与多款现有泛函数据排序方法的性能。结果表明，当数据受到白噪声干扰时，FP-OWA可显著提升排序一致性与稳定性。进一步地，本文将FP-OWA应用于2023年京津冀地区13个城市的日均PM2.5与O3浓度排序任务，精准揭示了区域污染的时空分异格局。上述研究成果为地方政府制定污染防治策略、改善空气质量提供了坚实的技术支撑。未来研究将聚焦于将FP-OWA拓展至高度非线性与复杂泛函数据场景，进一步提升其计算效率以适配大数据处理需求，并探索更多的应用场景。