Fuzzy equivalence relation clustering with transitive closure, transitive opening and the optimal transitive approximation

Abstract

In this paper, the fuzzy equivalence relation clustering is studied. Firstly, an algorithm for obtaining a transitive lower approximation or a suboptimal transitive approximation of a fuzzy similarity relation is given. Secondly, the relationship between fuzzy equivalence relation clustering and the agglomerative hierarchical clustering is investigated. Thirdly, a clustering method combining fuzzy equivalence relation clustering and fuzzy c-means clustering is proposed. Finally, numerical experiments are carried out to verify the algorithm.