STRUCTURE OF TRANSITIVE VALUED BINARY RELATIONS

The paper is concerned with the transitivity property of valued binary relations. A general representation theorem is established for any T- transitive valued binary relation, where T is a left-continuous triang ular norm. The study is carried out by using traces of valued binary r elations. Some results that have already been cited in the literature are shown to be consequences of the representation theorem. Maximal T- transitive relations contained in a given relation are also investigat ed and a procedure is developed to construct them.