Rough Approximations under Two Interpretations of Missing Values

Abstract

Rough sets are applied to data tables containing missing values under two interpretations where the missing values are probabilistically or possibilistically. A family of weighted equivalence classes is obtained for each interpretation, in which each equivalence class is accompanied by a degree to which it is an actual one. By using the family of weighted equivalence classes we can derive a lower approximation and an upper approximation. Results obtained under two interpretations of missing values are compared. For Lower and upper approximations, the possibliistic approximation by the necessity measure, the probabilistic approximation, the possibilistic approximation by the possibility measure arrange in ascending order.