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 (nn/2) 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). Our analysis of many DF-to-DNF conversion processes showed that approximately (1 − 2/(nn/2) × 100)% 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 0.5 × (nn/2) 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.