Application of the Hausdorff Fractal Grey Model to Predict Inhalable Particulate Matter and Carbon Dioxide Emissions Ratio in Turkey

The Grey model is a powerful tool for forecasting and modeling systems with incomplete or uncertain data. Its ability to generate accurate predictions with minimal data makes it particularly useful in various fields, including environmental studies. This study enhances the effectiveness of the Grey and Discrete Grey models by incorporating the Hausdorff fractal derivative. The model is applied to real-world data on air pollution, focusing on respirable particulate matter and carbon dioxide emissions. The data, obtained from recent references, have been carefully analysed and used to generate predictions. The predicted values are presented in tabular form, and the impact of applying the Hausdorff fractal derivative on the prediction accuracy under different conditions is demonstrated. The analysis of the data underlines the need for proactive measures to deal with air pollution in the future and highlights the importance of timely intervention to mitigate its adverse effects.