Performance of five methods under Spike 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.