In this paper we introduced direct product of intuitionistic fuzzy multigroups of G under norms(IF M SN (G)) and we prove that it will be also IF M SN (G). Next we shall study some important properties and theorems for them. On the other hand we shall give the definition of the identity element, strong upper- lower and weak upper- lowerof them and study the main theorem for this. We shall also give new results on this subject. Also we define the concepts of conjugate and commutative of IF M SN (G) and investigate them under direct product. Finally, we organize them under group homomorphisms and we prove that the image and preimage of direct product of IF M SN (G) will be also IF M SN (G).
Mathematical Analysis and Convex Optimization