Choquet-Based Fuzzy Rough Sets
This work addresses robustness issues in fuzzy rough sets for machine learning, offering a more flexible method that is incremental over existing OWA-based approaches.
The paper tackles the sensitivity of classical fuzzy rough sets to outliers by generalizing the OWA-based approach to Choquet-based fuzzy rough sets (CFRS), which maintains theoretical properties like duality and monotonicity and enables integration with outlier detection to enhance robustness in machine learning applications.
Fuzzy rough set theory can be used as a tool for dealing with inconsistent data when there is a gradual notion of indiscernibility between objects. It does this by providing lower and upper approximations of concepts. In classical fuzzy rough sets, the lower and upper approximations are determined using the minimum and maximum operators, respectively. This is undesirable for machine learning applications, since it makes these approximations sensitive to outlying samples. To mitigate this problem, ordered weighted average (OWA) based fuzzy rough sets were introduced. In this paper, we show how the OWA-based approach can be interpreted intuitively in terms of vague quantification, and then generalize it to Choquet-based fuzzy rough sets (CFRS). This generalization maintains desirable theoretical properties, such as duality and monotonicity. Furthermore, it provides more flexibility for machine learning applications. In particular, we show that it enables the seamless integration of outlier detection algorithms, to enhance the robustness of machine learning algorithms based on fuzzy rough sets.