Knowledge induction from uncertain information systems

Rough set theory is an important method to deal with imprecise and vague knowledge. However, one of the difficult problems of rule induction is that the classic rough set theory cannot extract rules from those information systems which include uncertain continuous attribute values. In this paper, a new rough set approach that integrates fuzzy set theory is presented to induce knowledge in this kind of information system. Fuzzy similarity relationis used as the base of similarity classification of each object in a universe and the definition of upper and lower approximation of an object set X subset of U is proposed. A decision table includes uncertain continuous data and is divided into two subtables for rules induction, one being a consistent decision subtable and the other a completely inconsistent decision subtable; two different new methods for the two subtables are proposed to induce decision rules. At the end of the paper, an example is given for further illustration.