Park C.Alaca C.2025-04-102025-04-102012http://hdl.handle.net/20.500.14701/50332The purpose of this article is to introduce the concept of 2-fuzzy n-normed linear space or fuzzy n-normed linear space of the set of all fuzzy sets of a non-empty set. We define the concepts of n-isometry, n-collinearity n-Lipschitz mapping in this space. Also, we generalize the Mazur-Ulam theorem, that is, when X is a 2-fuzzy nnormed linear space or ℑ(X) is a fuzzy n-normed linear space, the Mazur-Ulam theorem holds. Moreover, it is shown that each n-isometry in 2-fuzzy n-normed linear spaces is affine. © 2012 Park and Alaca.Article10.1186/1029-242X-2012-14