Rough set approach to incomplete data

Abstract

In this paper incomplete data are assumed to be decision tables with missing attribute values. We discuss two main cases of missing attribute values: lost values (a value was recorded but it is unavailable) and "do not care" conditions (the original values were irrelevant). Through the entire paper the same calculus, based on computations of blocks of attribute-value pairs, is used. Complete data are characterized by the indiscernibility relations, a basic idea of rough set theory. Incomplete data are characterized by characteristic relations. Using characteristic relations, lower and upper approximations are generalized for incomplete data. Finally, from three definitions of such approximations certain and possible rule sets may be induced.