Kryszkiewicz’s Formula for Indiscernibility of Missing Values

Abstract

When extracting any information from an information table with incomplete information, following Lipski we only know the lower and upper bounds of the information. Methods of rough sets that are applied to data tables containing incomplete information are examined from the viewpoint of Lipski’s approach based on possible world semantics. It is clarified that the formula that is first used by Kryszkiewicz, which most of the authors use, only gives the lower bound of the lower approximation and the upper bound of the upper approximation. This is due to that the formula considers only the indiscernibility of missing values with another value. We extend Kryszkiewicz’s formula by considering the discernibility of missing values. As a result, the extended Kryszkiewicz’s formula gives the same approximations as those in terms of Lipski’s approach.