A Tolerant Rough Set Approach for Handwritten Numeral Character Classification

This paper proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Similarity measure between two data is described by a distance function of all constituent attributes and they are defined to be tolerant when their similarity measure exceeds a similarity threshold value. The determination of optimal similarity theshold value is very important for the accurate classification. So, we determine it optimally by using the genetic algorithm (GA), where the goal of evolution is to balance two requirements such that (1) some tolerant objects are required to be included in the same class as many as possible. After finding the optimal similarity threshold value, a tolerant set of each object is obtained and the data set is grounded into the lower and upper approximation set depending on the coincidence of their classes. We propose a two-stage classification method that all data are classified by using the lower approxi ation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. We apply the proposed classification method to the handwritten numeral character classification. problem and compare its classification performance and learning time with those of the feed forward neural network's back propagation algorithm.