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In this paper, we propose the notion of fuzzy multigroups under t-norms. Some properties of them are explored and some related results are obtained. Also inverse, product, intersection and sum of them will be defined and investigated properties of them. Finally under group homomorphisms, image and pre image of them will be introduced and investigated.

In this paper, fuzzy subgroups on direct product of groups over a t-norm has been discussed. By using a t-norm T, we characterize some basic properties of T -fuzzy direct product of groups and normal T -fuzzy direct product of groups. Also we define the concept normal subgroups between T -fuzzy direct product of groups and prove some basic properties.