Rough Set Strategies to Data with Missing Attribute Values

In this paper we assume that a data set is presented in the form of the incompletely specified decision table, i.e., some attribute values are missing. Our next basic assumption is that some of the missing attribute values are lost (e.g., erased) and some are "do not care" conditions (i.e., they were redundant or not necessary to make a decision or to classify a case). Incompletely specified decision tables are described by characteristic relations, which for completely specified decision tables are reduced to the indiscernibility relation. It is shown how to compute characteristic relations using an idea of block of attribute-value pairs, used in some rule induction algorithms, such as LEM2. Moreover, the set of all characteristic relations for a class of congruent incompletely specified decision tables, defined in the paper, is a lattice. Three definitions of lower and upper approximations are introduced. Finally, it is shown that the presented approach to missing attribute values may be used for other kind of missing attribute values than lost values and "do not care" conditions.