Cluster analysis based on fuzzy relations

In this paper, cluster analysis based on fuzzy relations is investigated. Tamura's max-min n-step procedure is extended to all types of max-t compositions. A max-t similarity-relation matrix is obtained by beginning with a proximity-relation matrix based on the proposed max-t n-step procedure. Then a clustering algorithm is created for the max-t similarity-relation matrix. Three critical max-t compositions of max-min, max-prod and max-Delta are compared. The max-Delta composition is recommended as the first choice among them. Several examples give more perspectives for different choices of max-t compositions. Finally, the topic of incomplete data via max-t compositions is discussed. Max-t compositions can be effectively used to treat the t-connected incomplete data. (C) 2001 Elsevier Science B.V. All rights reserved.