Data classification based on tolerant rough set

Abstract 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 threshold 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 and (2) some objects in the same class are required to be tolerable as much as possible. After finding the optimal similarity threshold value, a tolerant set of each object is obtained and the data set is grouped 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 approximation 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. The validity of the proposed classification method is tested by applying it to the IRIS data classification and its classification performance and processing time are compared with those of other classification methods such as BPNN, OFUNN, and FCM.