on fuzzy small submodules and fuzzy direct sums of modules

In this paper, we investigate fuzzy small submodules of a module and their properties. we introduce fuzzy small epimorphisms and fuzzy small covers, and explore the behavior of fuzzy small submodules under direct sums and quotient modules. relations between fuzzy small submodules and classical small submodules, as well as the jacobson radical in the fuzzy setting, are also studied. several necessary and sufficient conditions for fuzzy small submodules are established, and we generalize well-known results on small submodules to the fuzzy context.