Expressing Rough Sets with Possibility Distributions in Possibilistic Data Tables

Rough sets are described in possibilistic data tables with values expressed in normal possibility distributions. A possibilistic data table is transformed into the set of incomplete data tables with possible degrees by using \(\alpha \) -cut. Every incomplete data table is dealt with from the viewpoint of possible world semantics used by Lipski and creates possible tables. In each possible table, we obtain the binary relation of object indiscernibility. Aggregating the binary relations we derive the minimum and maximum of approximations in a level of \(\alpha \) -cut. As a results, the minimum and the maximum of approximations are derived in the form of possibility distributions. The actual approximation exists between them. This representation allows us to grasp the overall picture of the approximations.