Forward approximation and backward approximation in fuzzy rough sets

It is general to obtain rules by attribute reduction in fuzzy information systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. Forward and backward approximations in fuzzy rough sets are first defined, and their important properties are discussed. Two algorithms based on forward and backward approximations, namely, mine rules based on the forward approximation (MRBFA) and mine rules based on the backward approximation (MRBBA), are proposed for rule extraction. The two algorithms are evaluated by several data sets from the UC Irvine Machine Learning Repository. The experimental results show that both MRBFA and MRBBA achieve better classification performances than the method based on attribute reduction.