In this paper we generalize Malik and Mordeson’s paper (1991). I analysis the Cartesian product of fuzzy subgroups (ideals ) of different groups (different ideals). That is ; if μ and σ are fuzzy subgroups (ideals) of G1 and G2 (R1 and R2 ) respectively then μ x σ is a fuzzy subgroup (ideal) of G1 x G2 ( ). Conversely the opposite direction of the above statements is studied. We generalize above statements for different Groups (Rings).