Constraint-based attribute reduction in rough set analysis

Attribute reduction is very important in rough set-based data analysis (RSDA) because it can be used to simplify the induced decision rules without reducing the classification accuracy. The notion of reduct plays a key role in rough set-based attribute reduction. In rough set theory, a reduct is generally defined as a minimal subset of attributes that can classify the same domain of objects as unambiguously as the original set of attributes. Nevertheless, from a relational perspective, RSDA relies on a kind of dependency constraint. That is, the relationship between the class labels of a pair of objects depends on the componentwise comparison of their condition attributes. The larger the number of condition attributes compared, the greater the probability that the constraint will hold. Thus, elimination of condition attributes may cause more object pairs to violate the constraint. Based on this observation, a reduct can be defined alternatively as a minimal subset of attributes that does not increase the number of objects violating the constraint. While the alternative definition coincides with the original one in ordinary RSDA, it is more easily generalized to cases of fuzzy RSDA and relational data analysis.