Rough Sets and Functional Dependencies in Data: Foundations of Association Reducts

We investigate the notion of an association reduct. Association reducts represent data-based functional dependencies between the sets of attributes, where it is preferred that possibly smallest sets determine possibly largest sets. We compare the notions of an association reduct to other types of reducts previously studied within the theory of rough sets. We focus particularly on modeling inexactness of dependencies, which is crucial for many real-life data applications. We also study the optimization problems and algorithms that aim at searching for the most interesting approximate association reducts in data.