Optimization methods for fuzzy clustering

✍ Scribed by Fu Guoyao

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 470 KB
• Volume: 93
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(96)00227-8

✦ Synopsis

As known, the clustering data obtained by the paired comparisons or questionnaires are symmetric and can be represented by a fuzzy symmetric and reflexive matrix B which is called to a fuzzy similarity matrix in this paper. In general, they do not necessarily satisfy the fuzzy transitive condition which is very essential for clusterings. Now the transitive relations are always obtained by taking the transitive closure A from the intransitive clustering data B. Recently, the idea of optimal fuzzy equivalent matrix, i.e. a fuzzy transitive similarity matrix with the smallest distance from B, has been proposed. It is the best transitive expression in the sense of the minimum deviation and its efficiency is better than that of A. This paper shows the structure of a fuzzy transitive similarity matrix, and then an algorithm for calculating the global optimal fuzzy equivalent matrix is presented. Finally, it is pointed out that the global optimal fuzzy equivalent matrix must exist, but is not unique.