On the Mazur-Ulam theorem in non-Archimedean fuzzy \(n\)-normed spaces (Q2449012)

Summary: The motivation of this paper is to present a new notion of non-Archimedean fuzzy \(n\)-normed space over a field with valuation. We obtain a Mazur-Ulam theorem for fuzzy \(n\)-isometry mappings in the strictly convex non-Archimedean fuzzy \(n\)-normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the corresponding triangle. And then, using this result, we get a Mazur-Ulam theorem for the interior preserving fuzzy \(n\)-isometry mappings in non-Archimedean fuzzy \(n\)-normed spaces over a linear ordered non-Archimedean field.