Representation of Fuzzy Symmetric Relations

摘要

The representation theorem for F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F-transitive fuzzy relations on a set X, F being an Archimedean t-norm, is dense in the set of Z-transitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.