Fuzzy differential invariant (FDI)

In this paper, we have tried to apply the concepts of fuzzy set to Lie groups and fuzzy differential invariant (FDI) in order to provide suitable conditions for applying Lie symmetry method in solving fuzzy differential equations (FDEs). For this, we define a C1-fuzzy submanifold and fuzzy immersion with some examples. In main section, we defined the fuzzy Lie group and some its relative concepts such as fuzzy transformation group and fuzzy Ginvariant. The goal of this paper is to introduce and study new defining for fuzzy Lie group and fuzzy differential invariant (FDI). Also, some illustrative examples are given.