J. Jacas and L. Valverde
The representation theorem for fuzzy transitive relations has become a powerful tool to build fuzzy transitive relations from arbitrary fuzzy subsets of a given set. Its applicability rests essentially on facts such as its constructive form, the little distortion it produces on the data and the possibility to compress -through a convenient set of generators- the information on the structure of the data conveyed by the relation. On the other hand, the duality between fuzzy transitive relations and a kind of pseudometrics allows to introduce -in rather a natural way- (fuzzy) classifications associated with such pseudometrics. All these concepts and results are reviewed in this work.