Applying rough sets to data tables containing missing values

Rough sets are applied to data tables containing missing values. Discernibility and indiscernibility between a missing value and another value are considered simultaneously. A family of possible equivalence classes is obtained, in which each equivalence class has the possibility that it is an actual one. By using the family of possible equivalence classes, we can derive lower and upper approximations, even if the approximations are not obtained by previous methods. Furthermore, the lower and upper approximations coincide with those obtained from methods of possible worlds.