Clustering using Similarity Upper Approximation

Rough set theory operates on an information system that consists of a set of objects. A core concept of rough set theory is that of equivalence between objects called indiscernibility. Indiscernibility reflects a total impossibility of distinguishing between objects, considering the available information. Considering a tolerance or similarity relation instead of an indiscernibility relation is quite relevant due to the existence of quantitative attributes in the information systems. Extending indiscernibility to tolerance relation results in weakening of some of the properties of the binary relation in terms of reflexivity, symmetry and transitivity. In this paper, we present a clustering technique using similarity relation with transitivity property being relaxed. The concept of similarity upper approximation has been used to form the initial family of cluster. A relationship based measure has been used to decide the belongingness of uncertain elements. We present an example to illustrate our proposed methodology. This promises to be a useful and interesting area of extension of the theory of rough sets.