Fuzzy Rough Sets with GA-Based Attribute Division

–Rough set theory is a powerful tool to extract classification rules from a database that usually is given in the form of information system in which information is expressed by attributes and their values. In this paper, we first evaluate every example data (tuple) using, not a singleton but, a fuzzy number (or, suppose the original information system is along with such fuzzy numbers), due to the fact that the fuzzy numbers are easily set in comparison with the singletons. Then, based on the information system with the fuzzy numbers, we give a new definition of fuzzy rough set. As a result, the traditional rough set proposed by Z. Pawlak is a special case of the fuzzy rough set. Consequently, the upper/lower approximation, which is corresponding with the negative/positive rules, is varying based on the system uncertainties. At the same time, the possible rules can be reduced whereas the negative/positive rules are increased. It means that the approximation precision is improved. In addition, the genetic algorithm is adopted to divide the attribute values that have continuous values into the most proper discrete values in order to improve the approximateness of the system. Key-Words:– Rough sets, information system, rule extraction, fuzzy sets, fuzzy rough sets, genetic algorithm.