Applying Rough Sets to Information Tables Containing Missing Values

Several methods of rough sets that are applied to data tables containing missing values are examined from the viewpoint of the method of possible worlds. It is clarified that the previous methods do not give the same results as the method of possible worlds. This is due to that the previous methods consider either of indicernibility or discernibility of missing values.In order to improve this point, a new method, called a method of possible equivalence classes, is described. By using possible equivalence classes, both indiscernibility and discernibility of missing values are taken into account. As a result, the method of possible equivalence classes gives the same results as the method of possible worlds.In addition, by using the maximal possible equivalence classes, not all possible equivalence classes, rough approximations are efficiently obtained.