Multi-class decision-theoretic rough sets

• We provides a new formulation of multi-class decision-theoretic rough sets.
• A three-way decision is made to each class.
• Different types of misclassification errors are treated separately based on the notion of loss functions.
• This approach is well suited for cost-sensitive classification tasks.
• The connections and differences with other existing multi-class rough set models are analyzed.

As a natural extension to rough set approximations with two decision classes, this paper provides a new formulation of multi-class decision-theoretic rough sets. Instead of making an immediate acceptance or rejection decision, a third option of making a deferment decision is added to each class. This gives users the flexibility of further examining the suspicious objects, thereby reducing the chance of misclassification. Different types of misclassification errors are treated separately based on the notion of loss functions from Bayesian decision theory. The losses incurred for making deferment and rejection decisions to each class are also considered. The presented approach appears to be well suited for cost-sensitive classification tasks where different types of classification errors have different costs. The connections and differences with other existing multi-class rough set models are analyzed.