We examined dual properties of traces of a fuzzy relation using fuzzy matrices. Traces of a fuzzy relation are reflexive and transitive fuzzy relations obtained from the given fuzzy relation. Under standard operations on fuzzy matrices, fuzzy matrix inequalities and equalities are deduced by applying the well-known equivalent transformation of a fuzzy matrix inequality. We present, in particular, propositions on the construction of transitive fuzzy relations.
Keywords: fuzzy matrix, fuzzy matrix inequality, fuzzy relation, trace of a fuzzy relation