GBFRS: Robust Fuzzy Rough Sets via Granular Ball Computing

Area of Science:

• Data Science
• Machine Learning
• Artificial Intelligence

Background:

• Fuzzy Rough Set (FRS) theory effectively handles data uncertainty but struggles with noise due to pointwise analysis.
• Existing FRS models lack robustness against noisy data, limiting their practical application in complex datasets.

Purpose of the Study:

• To propose a novel Granular Ball Fuzzy Rough Set (GBFRS) framework for enhanced feature selection.
• To improve the noise tolerance and robustness of FRS models by integrating granular ball computing.

Main Methods:

• Replaced individual data points with granular balls of varying sizes in the FRS framework.
• Labeled each granular ball by the majority class of its internal samples to mitigate noise impact.
• Redefined a weighted fuzzy dependency function, assigning weights based on the proportion of samples within each granular ball.

Main Results:

• The GBFRS framework demonstrated improved noise tolerance and robustness compared to traditional FRS methods.
• Experimental results on UCI datasets showed that GBFRS achieved superior classification accuracy.
• Theoretical foundations, including approximation properties and dependency convergence, were formally established.

Conclusions:

• The proposed GBFRS framework offers a more stable and accurate approach to feature selection in uncertain and noisy datasets.
• GBFRS effectively addresses the limitations of existing FRS models, paving the way for more reliable data analysis.
• The study provides open-source code and datasets for reproducibility and further research.