Direct product of fuzzy multigroups under t -norms

This paper proposes the concept of direct product of fuzzy multigroups under
t
-norms and some of their basic properties are obtained. Next, we investigate and obtain some new results of strong upper alpha-cut, weak upper alpha-cut, strong lower alpha-cut and weak lower alpha-cut of them. Later, we prove conjugation and commutation between them. Finally, the notion of homomorphism in the context of fuzzy multigroups was defined and some homomorphic properties of fuzzy multigroups under
t
-norms in terms of homomorphic images and homomorphic preimages, respectively, were presented.