Choquet-Based Fuzzy Rough Sets
Adnan Theerens, Oliver Urs Lenz, Chris Cornelis
TL;DR
Choquet-based fuzzy rough sets (CFRS) extend OWAFRS by employing the Choquet integral with monotone measures to compute lower and upper approximations, enabling non-additive and non-symmetric aggregation that improves robustness to outliers. The framework preserves essential properties like monotonicity and duality, while enabling integration with outlier detection through measures such as fuzzy removal and WOWA-based aggregations. Vague quantification links CFRS to linguistic quantifiers, providing intuitive interpretations of the approximations, and the method is demonstrated in classification tasks with experiments on 18 UCI datasets showing improved performance over OWAFRS baselines. Overall, CFRS offers a flexible, robust approach to fuzzy rough-set-based learning with practical utility for outlier-prone data scenarios.
Abstract
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.