Learning fuzzy rules from fuzzy samples based on rough set technique

Although the traditional rough set theory has been a powerful mathematical tool for modeling incompleteness and vagueness, its performance in dealing with initial fuzzy data is usually poor. This paper makes an attempt to improve its performance by extending the traditional rough set approach to the fuzzy environment. The extension is twofold. One is knowledge representation and the other is knowledge reduction. First, we provide new definitions of fuzzy lower and upper approximations by considering the similarity between the two objects. Second, we extend a number of underlying concepts of knowledge reduction (such as the reduct and core) to the fuzzy environment and use these extensions to propose a heuristic algorithm to learn fuzzy rules from initial fuzzy data. Finally, we provide some numerical experiments to demonstrate the feasibility of the proposed algorithm. One of the main contributions of this paper is that the fundamental relationship between the reducts and core of rough sets is still pertinent after the proposed extension.