cc -reduction in a fully fuzzy information system

Abstract

Attribute reduction is an important issue in knowledge discovery and data mining. Applying rough set theory, information systems based on crisp (or explicit) features can be easily done attribute reductions, but there exists rarely deeper discussion about attribute reduction in fuzzy information systems (i.e. information systems based on vague or undefinable features). A fully fuzzy information system is an information system where each of its attributes determines a fuzzy set on the object set, this paper investigates cc-reduction in this information system. The concept of class-consistent is first introduced. Then, the class-consistent relation cc(P) induced by the given attribute subset P in a fully fuzzy information system is proposed. Next, the class-consistent reduction (for short, cc-reduction) in a fully fuzzy information system is proposed and studied along with its corresponding algorithm. Moreover, considering that homomorphism is a kind of tools to study relationships between two fully fuzzy information systems, invariant characterizations of fully fuzzy information systems under homomorphisms are obtained. Finally, a numerical experiment is employed to illustrate the practical significance and possible applications of cc-reduction in a fully fuzzy information system.