A New Rough Set Classifier for Numerical Data Based on Reflexive and Antisymmetric Relations

The grade-added rough set (GRS) approach is an extension of the rough set theory proposed by Pawlak to deal with numerical data. However, the GRS has problems with overtraining, unclassified and unnatural results. In this study, we propose a new approach called the directional neighborhood rough set (DNRS) approach to solve the problems of the GRS. The information granules in the DNRS are based on reflexive and antisymmetric relations. Following these relations, new lower and upper approximations are defined. Based on these definitions, we developed a classifier with a three-step algorithm, including DN-lower approximation classification, DN-upper approximation classification, and exceptional processing. Three experiments were conducted using the University of California Irvine (UCI)'s machine learning dataset to demonstrate the effect of each step in the DNRS model, overcoming the problems of the GRS, and achieving more accurate classifiers. The results showed that when the number of dimensions is reduced and both the lower and upper approximation algorithms are used, the DNRS model is more efficient than when the number of dimensions is large. Additionally, it was shown that the DNRS solves the problems of the GRS and the DNRS model is as accurate as existing classifiers.