Cluster Analysis Based onT-transitive Interval-Valued Fuzzy Relations

Abstract

In this paper, we consider cluster analysis based on T-transitive interval-valued fuzzy relations. A fuzzy relation with its partitional tree for obtaining an agglomerative hierarchical clustering has been studied and applied. In general, these fuzzy-relation-based clustering approaches are based on real-valued memberships of fuzzy relations. Since interval-valued memberships may be better than real-valued memberships to represent higher order imprecision and vagueness for human perception, in this paper we first extend fuzzy relations to interval-valued fuzzy relations and then construct a clustering algorithm based on the proposed T-transitive interval-valued fuzzy relations. We use two examples to demonstrate the efficiency and usefulness of the proposed method. In practical application, we apply the proposed clustering method to performance evaluations for academic departments of higher education by using actual engineering school data in Taiwan.