A Unified Air Quality Assessment Framework Based on Linear Fuzzy Space Theory

Air quality is one of the most critical issues that humankind is facing today. There are diverse types of indices measuring air pollution, which are mostly based on aggregation functions. This paper proposes a model aimed at forecasting aggregated air pollution indices, which enables modelling data uncertainties. The proposed original model consists essentially of two sub models. The first one models Air Quality Index (AQI), while the second one models concentrations of pollutants. Multi-contaminant air quality index is modelled as an aggregation of the Pollutant Standard Index (PSI) obtained via fuzzy linear transformation defined by fuzzy breakpoints. We model concentrations of pollutants by regression (XGBoost, Deep Neural Network, ADA Boost, and Histogram Gradient Boosting Regressor) using fuzzy time series of two groups of data (pollutants’ concentrations and meteorological parameters). In doing so, the target variable was modeled in two ways. The first model is a set of independent classes defined by proper fuzzy membership functions, while the second one is a set of classes connected by an ordering relation. Simulation results are presented showing the model performance for each of the target variable models in terms of prediction mean absolute errors. The main result of the paper is a unified model of air quality assessment relying upon a consistent mathematical theory called Linear fuzzy space.