Fuzzy Lie Groups

In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a ${\mathcal{C}}^1$ fuzzy submanifold after reviewing ${\mathcal{C}}^1-$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.