Quantifying Group Fairness with Fuzzy-Rough Sets in Pattern Classification Problems

In this paper, we reformulate the recently introduced individual bias measure, Fuzzy-rough Uncertainty (FRU), such that it quantifies group-based bias. The FRU measure was originally made to quantify the changes on the boundary regions of a fuzzy-rough set caused by the removal of a protected feature from the data. Its intuition is that, in fair decision-making scenarios, removing a protected feature should not cause big changes in the decision boundaries of a fuzzy-rough set and the extent to which that happens can be understood as bias. The proposed reformulation of the FRU aggregates changes in the boundary regions for instances that belong in different groups. The difference between the FRU for each group can be understood as group-based bias. We test our proposed group-FRU on the Adult dataset and three synthetic datasets. For Adult dataset, results show that, on a group level, FRU captures the opposite trend compared to baseline measures, that is, more disparity between white and black people compared to males and females. Finally, the results on the synthetic datasets showed that the group-FRU can capture group-based bias.