An Improvement of β-Reduct and its Computation in Variable Precision Rough Set Model

Abstract

In this paper, we propose an improvement of β-reduct as a new minimal set of condition attributes called β-reduct in the variable precision rough sets (VPRS). VPRS has various kinds of reducts such as β-reduct and L^β-reduct based on structure-enhancing approach. The difference between these reducts depends on the focus such as quality of approximation and set-inclusion relationship of lower approximation. β-reduct we propose can extract minimal sets of condition attributes with higher evaluation values of quality of approximation better than the case that all condition attributes are used. We show theoretical relationships between β-reduct and relative reduct in Pawlak rough sets, and between β-reduct and β-reduct. We also propose a heuristic method to compute a candidate of β-reducts.