Decision bireducts and approximate decision reducts: Comparison of two approaches to attribute subset ensemble construction

We discuss the notion of a decision bireduct [1], which is an extension of the notion of a decision reduct developed within the theory of rough sets. We show relationships between the decision bireducts and some formulations of approximate decision reducts summarized in [2]. We investigate advantages of the decision bireducts and the approximate decision reducts within a rough-set-inspired framework for deriving attribute subset ensembles from data, wherein each of attribute subsets yields a single classifier, basically by generating its corresponding if-then decision rules from the training data. We also show how to use the above-mentioned relationships to build even more efficient rough-set-based ensembles in the future.