Similarity Based Rough Sets with Annotation

In the authors’ previous research the possible usage of the correlation clustering in rough set theory was investigated. Correlation clustering relies on a tolerance relation. Its result is a partition. From the similarity point of view singleton clusters have no information. A system of base sets can be generated from the partition, and if the singleton clusters are left out, then it is a partial approximation space. This way the approximation space focuses on the similarity (the tolerance relation) itself and it is different from the covering type approximation space relying on the tolerance relation. In this paper the authors examine how the partiality can be decreased by inserting the members of some singletons into an arbitrary base set and how this annotation affects the approximations. The authors provide software that can execute this process and also helps to select the destination base set and it can also handle missing data with the help of the annotation.