Quick general reduction algorithms for inconsistent decision tables

In the Pawlak rough set model, attribute reduction plays one of the important roles, and the preservation of different properties of the original decision table leads to different types of reduct definitions, such as relative relation reduct, positive-region reduct, distribution reduct, maximum distribution reduct, and assignment reduct. However, there are no general quick reduction approaches for obtaining various types of reducts; this motivated us to conduct the present study. We first establish a unified decision table model for five representative reducts in inconsistent decision tables, study the relative discernibility and relative discernibility reduct for the general decision table, and derive the corresponding properties. Then, two general reduction algorithms (GARA-FS△ and GARA-BS△) from the viewpoint of the relative discernibility in inconsistent decision tables are presented. Subsequently, to increase the efficiency of algorithms, two quick general reduction algorithms (QGARA-FS△ and QGARA-BS△) are proposed mainly by reducing the sort times to increase the efficiency of reduction algorithms. Finally, a series of experiments with UCI data sets are conducted to evaluate the effectiveness and performance of the proposed reduction algorithms.