Similarity Based Granules

In the authors’ previous research, a possible usage of the correlation clustering in rough set theory was investigated. Correlation clustering is based on a tolerance relation and its output is a partition. The system of granules can be derived from the partition and as a result, a new approximation space appears. This space focuses on the similarity (represented by a tolerance relation) itself and it is different from the covering type approximation space relying on a tolerance relation. In real-world applications, the number of objects is very high. So it can be effective only if a portion of the data points is used. Previously we provided a method that chooses the necessary number of objects that represent the data set. These members are called representatives and it can be useful to apply them in the approximation of an arbitrary set. A new approximation pair can be defined based on the representatives. In this paper, some very important properties are checked for this approximation pair and the system of granules.