  This paper introduces a novel Choquet distance using fuzzy rough set based
measures. The proposed distance measure combines the attribute information
received from fuzzy rough set theory with the flexibility of the Choquet
integral. This approach is designed to adeptly capture non-linear relationships
within the data, acknowledging the interplay of the conditional attributes
towards the decision attribute and resulting in a more flexible and accurate
distance. We explore its application in the context of machine learning, with a
specific emphasis on distance-based classification approaches (e.g. k-nearest
neighbours). The paper examines two fuzzy rough set based measures that are
based on the positive region. Moreover, we explore two procedures for
monotonizing the measures derived from fuzzy rough set theory, making them
suitable for use with the Choquet integral, and investigate their differences.
