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<p><b>Abstract</b>—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 nonclassified 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 feedforward neural network's backpropagation algorithm.</p>
Tolerant rough set, lower and upper approximation, similarity measure, genetic algorithms, handwritten numeral character classification.

D. Kim and S. Bang, "A Handwritten Numeral Character Classification Using Tolerant Rough Set," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 22, no. , pp. 923-937, 2000.
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