Fast Feature Selection in Interval Data Using Rough Sets with Fuzzy Tolerance Relation-Based Hierarchical Approximations

As a highly active research field, feature selection plays a critical role in multi-criteria decision making, hierarchical data analysis, and artificial intelligence. Rough set (RS) theory, presented by Pawlak, is a useful and important methodology for feature selection. Discernibility matrix-based and heuristic methods are two important rough set approaches for feature selection in interval-valued data. However, they still face significant computational challenges when dealing with high-dimensional and large-scale interval-valued data. To improve the efficiency of feature selection in an interval-valued decision system (IvDS), we construct a hierarchical approximation model and establish the corresponding theoretical results based on the fuzzy tolerance relation, which is symmetric and reflexive. Based on this model, we explore the order-preservation property of attribute significance in an IvDS and achieve attribute reduction on a gradually decreasing universe, which improves the efficiency of feature selection. Motivated by this idea, we develop two fast algorithms, named FFSDF and FFSCE. The proposed algorithms can achieve higher efficiency while preserving the same reduction results as the original feature selection algorithms. Finally, experiments are conducted on fifteen datasets to demonstrate that the proposed fast algorithms are more effective and efficient.