Incomplete information tables and rough classification

The rough set theory, based on the original definition of the indiscernibility relation, is not useful for analysing incomplete information tables where some values of attributes arc unknown. In this paper we distinguish two different semantics for incomplete information: the missing value semantics and the absent value semantics. The already known approaches, e.g. based on the tolerance relations, deal with the missing value case. We introduce two generalisations of the rough sets theory to handle these situations. The first generalisation introduces the use of a non symmetric similarity relation in order to formalise the idea of absent value semantics. The second proposal is based on the use of valued tolerance relations. A logical analysis and the computational experiments show that for the valued tolerance approach it is possible to obtain more informative approximations and decision rules than using the approach based on the simple tolerance relation.