Attribute reduction based on classes in incomplete ordered decision systems

Dominance-based rough set approach (DRSA) has attracted much attention in multi-criteria decision-making problems for data with preference-ordered relations since its inception. However, in the real world, there is often the challenge of incomplete information. This paper addresses approaches to attribute reduction in an incomplete ordered decision system (IODS). Attribute evaluation is crucial in the attribute reduction process. Traditional evaluation functions primarily depend on the relationships between features, neglecting their impact on classification, and incur high computational costs when calculating lower and upper approximations. To address these issues, this paper proposes whole inter-class non-dominance as the criterion for attribute importance. First, we define the concepts of inter-class proximity and inter-class non-dominance in an IODS, with whole inter-class non-dominance serving as the evaluation index for attribute importance. Next, we propose a method for calculating inter-class non-dominance based on the expanded dominance matrix. Finally, combined with the heuristic search strategy, an attribute reduction algorithm based on inter-class non-dominance (HANDR) was designed, and experiments on various datasets from the University of California at Irvine (UCI) demonstrate that the proposed algorithm significantly improves running time and classification accuracy.