Clustering with vague set

Abstract

This article constitutes a new method of clustering. The classical concept of fuzzy logic provides the means to represent approximate knowledge. Therefore the elements which lie in the boundaries of several sets are forced to belong to any of the sets. Introduction to fuzzy sets undoubtedly increases the computational burden, so there is an extension into shadowed sets, which takes the essence of fuzzy sets and reduce the computational complexity of the fuzzy sets. Shadowed set is based on three valued logic which represents the concept of full exclusion(0), full participation(1) and uncertain. So a shadowed set comprises of the elements with full participation in the set and those which are uncertain of this set. Here we have used another set theoretic concept named as vague set, it changes the general concept of fuzzy set and it removes the uncertainty of the shadowed set. Each object of this vague set has a grade of membership whose value is a continuous sub interval of [0,1]. In this study we have proposed a set theoretic concept which combines the concept of shadowed set as well as vague set. We use the proposed concept for the clustering of synthetic data sets and real data sets. The experimental results are analyzed by both quantitative and qualitative measures.