The concept of algebra fuzzy was initially introduced by Rosenfeld in 1971. In 1991, Malik and Moderson explained if cartesian product of two fuzzy subgroup from same group, then it was fuzzy subgroup too and if cartesian product of two fuzzy ideal from same ring, then it was fuzzy ideal too. We discuss the cartesian product of two or more fuzzy subgroups from different group, then it was fuzzy subgroup too and cartesian product of two or more fuzzy ideal from different ring, then it was fuzzy ideal too.
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