A logic method for efficient reduction of the space complexity of the attribute reduction problem

The goal of attribute reduction is to find a minimal subset (MS) R of the condition attribute set C of a dataset such that R has the same classification power as C. It was proved that the number of MSs for a dataset with n attributes may be as large as Mathematical equation represented and the generation of all of them is an NP-hard problem. The main reason for this is the intractable space complexity of the conversion of the discernibility function (DF) of a dataset to the disjunctive normal form (DNF). Ouranalysis of many DF-to-DNF conversion processes showed that approximately Mathematical equation represented of the implicants generated in the DF-to-DNF process are redundant ones. We prevented their generation based on the Boolean inverse distribution law. Due to this property, the proposed method generates Mathematical equation represented times fewer implicants than other Boolean logic-based attribute reduction methods. Hence, it can process most of the datasets that cannot be processed by other attribute reduction methods. © TÜBITAK.