Many papers about Fuzzy algebra have been published since A. Rosenfeld presented the concept of Fuzzy subgroups in 1971. As further work in this respect，we study the direct sum of Fuzzy subrings in this paper，introduce the concepts of projective Fuzzy sets and marginal Fuzzy sets of direct sum rings，and abtain a necessary and sufficient condition that a Fuzzy subring on the direct sum of rings may be represented by the direct sum of Fuzzy subrings on each ring. Finally，a similar discussion of t-Fuzzy subrings is suggested.