  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.
