Rough set based non metric model

This paper proposes a new non metric model algorithm based on rough set. Non metric model is a kind of clustering methods, in which the belongingness of an object to each cluster is directly calculated from the dissimilarities between objects. It means that the cluster centers are not used and the data space is not restricted to Euclidean space. On the other hand, rough set is a representation of obscure belongingness of an object to a set and a rough set consists of a lower and an upper approximations of the original set. The former is a set of objects which are completely included in the original set and the latter is a set of objects which are possibly included in the original set. Rough set representation has been applied to clustering. The clustering is called rough clustering. In rough clustering, the lower approximation and upper approximation mean that an object `necessarily´ and `possibly´ belongs to cluster, respectively. Thus, the indiscernible object should be classified into two or more upper approximations. This paper constructs a new non metric model algorithm based on rough set and verifies the performance of the proposed algorithm through some numerical examples.