Irreducible descriptive sets of attributes for information systems

The maximal consistent extension Ext(S) of a given information system S consists of all objects corresponding to attribute values from S which are consistent with all true and realizable rules extracted from the original information system S. An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B. We show that there exists only one irreducible descriptive set of attributes. We present a polynomial algorithm for this set construction. We also study relationships between the cardinality of irreducible descriptive set of attributes and the number of attributes in S. The obtained results will be useful for the design of concurrent data models from experimental data. © 2010 Springer-Verlag.