Cost-sensitive fuzzy rough learning for multi-class imbalanced data classification

Yang Tian

doi:10.1016/j.ijar.2026.109784

Cost-sensitive fuzzy rough learning for multi-class imbalanced data classification

2026-07-01

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DOI：10.1016/j.ijar.2026.109784

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Imbalanced data presents significant challenges in many real-world applications, where the minority class often holds critical importance but is underrepresented. It becomes more complex when the data involves multiple classes. Numerous methods are currently available for multi-class imbalance problems. However, most of them convert the problem into multiple binary classification tasks, making it challenging to fully capture the original distribution of multi-class data. This paper aims to address the problem by proposing a fuzzy rough set-based method, which focuses on the intrinsic relationships between the classes and features (class-feature relationships). To overcome the limitations of euclidean distance in imbalanced datasets which is sensitive to the scale of individual features, we introduce the standardized euclidean distance and propose a corresponding fuzzy rough set based on it. Using the lower and upper approximation operators, we define the intra-class and inter-class determinacies of samples for each individual feature, and fuse them into a predictive membership by weighting each feature's importance. Combining this with a cost-sensitive strategy, we formulate a cost-weighted objective function that is trivially solvable via the classical gradient method, enabling efficient weight adaptation and the development of learning algorithms. After that, the prediction algorithm is proposed by using the optimal weights and the corresponding cost vector. Numerical experiments on 13 imbalanced datasets against 8 representative algorithms demonstrate the effectiveness of the proposed method.

Keywords:

Fuzzy rough set

Imbalanced classification

Multi-class tasks

Cost-sensitive learning

Cost-sensitive fuzzy rough learning for multi-class imbalanced data classification

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