Choquet-Based Fuzzy Rough Sets

TL;DR

This paper introduces Choquet-based fuzzy rough sets, generalizing OWA-based approaches to improve robustness and flexibility in machine learning, especially for handling outliers and inconsistent data.

Contribution

It extends fuzzy rough set theory by incorporating Choquet integrals, providing a more flexible framework that maintains key properties and enhances outlier detection capabilities.

Findings

Maintains duality and monotonicity in the generalized model

Enables integration of outlier detection algorithms

Improves robustness of machine learning with fuzzy rough sets

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.