  In this paper, we have tried to apply the concepts of fuzzy sets to Lie
groups and its relative concepts. First, we define a ${\cal C}^1$ fuzzy
submanifold after reviewing ${\cal C}^1-$fuzzy manifold definition. In main
section, we defined the Lie group and some its relative concepts such as fuzzy
transformation group, fuzzy $G$-invariant. Our aim is to prepare the suitable
conditions for defining fuzzy differential invariant by constructing suitable
objects.
