Incorporating Grey Total Influence into Tolerance Rough Sets for Classification Problems

Tolerance-rough-set-based classifiers (TRSCs) are known to operate effectively on real-valued attributes for classification problems. This involves creating a tolerance relation that is defined by a distance function to estimate proximity between any pair of patterns. To improve the classification performance of the TRSC, distance may not be an appropriate means of estimating similarity. As certain relations hold among the patterns, it is interesting to consider similarity from the perspective of these relations. Thus, this study uses grey relational analysis to identify direct influences by generating a total influence matrix to verify the interdependence among patterns. In particular, to maintain the balance between a direct and a total influence matrix, an aggregated influence matrix is proposed to form the basis for the proposed grey-total-influence-based tolerance rough set (GTI-TRS) for pattern classification. A real-valued genetic algorithm is designed to generate the grey tolerance class of a pattern to yield high classification accuracy. The results of experiments showed that the classification accuracy obtained by the proposed method was comparable to those obtained by other rough-set-based methods.