A kind of approximations of generalized rough set model
In this paper, we investigate the approximation problem of generalized rough set model. In generalized rough sets, the binary relation on one universe is always unknown and needed to be induced by the other already-known relation. In order to evaluate the induced binary relation, we propose a pair of generalized approximations called generalized lower and upper approximations by which the induced binary relation and the already-known binary relation can be connected. We also assert that the pair of generalized approximations are related to the definitions of approximations of classical rough sets. Their algebraic properties and topology structures are first studied. More important, we both give some comparisons of the relations in the same generalized rough set model and the approximations among different generalized rough set models. In the end, some applications of the proposed approximations in covering based rough sets are presented.
approximation generalized rough set rough set generalized approximation covering