The Generalized Model Of Rough Set Theory

Although rough set theory is a powerful tool dealing with incompleteness and uncertainty, its performance to deal with initial fuzzy data is poor. In this paper we make an attempt to improve the performance of existing rough sets model via fuzzy similarity relation. From both knowledge representation and knowledge reduction, we generalize rough sets to fuzzy environments. Consider the similarity of objects we define fuzzy lower, upper approximation and fuzzy rough sets. Furthermore, we generalize a series of concepts of knowledge reduction to fuzzy environment, and then propose a heuristic algorithm which give a fuzzy and dynamic process to deal with initial fuzzy data. Finally the numerical example illustrates that the proposed approach in this paper can obtain some simple fuzzy production rules.