Incomplete information tables and rough classification

The rough set theory, based on the original definition of the indiscernibil ity relation, is not useful for analysing incomplete information tables whe re some values of attributes arc unknown. In this paper we distinguish two different semantics for incomplete information: the "missing value" semanti cs and the "absent value" semantics. The already known approaches, e.g. bas ed on the tolerance relations, deal with the missing value case. We introdu ce 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 seco nd proposal is based on the use of valued tolerance relations. A logical an alysis and the computational experiments show that for the valued tolerance approach it is possible to obtain more informative approximations and deci sion rules than using the approach based on the simple tolerance relation.