Rule-preserved object compression in formal decision contexts using concept lattices

Rule acquisition is one of the main purposes in the analysis of formal decision contexts. In general, given a formal decision context, some of its objects may not be essential to the rule acquisition. This study investigates the issue of reducing the object set of a formal decision context without losing the decision rule information provided by the entire set of objects. Using concept lattices, we propose a theoretical framework of object compression for formal decision contexts. And under this framework, it is proved that the set of all the non-redundant decision rules obtained from the reduced database is sound and complete with respect to the initial formal decision context. Furthermore, a complete algorithm is developed to compute a reduct of a formal decision context. The analysis of some real-life databases demonstrates that the proposed object compression method can largely reduce the size of a formal decision context and it can remove much more objects than both the techniques of clarified context and row reduced context.