Mazur-Ulam type theorems for fuzzy normed spaces

In this paper, we provide Mazur-Ulam type results for (not necessarily surjective) maps preserving equality of fuzzy distance defined between two fuzzy normed spaces. Our main goal is to study the additivity of such generalizations of fuzzy isometries. As in the classical case, the fuzzy strict convexity of the target space will play an important role.