A generalized Mazur-Ulam theorem for fuzzy normed spaces (Q1724575)

Summary: We introduce \textit{fuzzy norm-preserving} maps, which generalize the concept of fuzzy isometry. Based on the ideas from \textit{A. Vogt} [Stud. Math. 45, 43--48 (1973; Zbl 0222.46015)] and \textit{J. Väisälä} [Am. Math. Mon. 110, No. 7, 633--635 (2003; Zbl 1046.46017)], we provide the following generalized version of the Mazur-Ulam theorem in the fuzzy context: let \(X\), \(Y\) be fuzzy normed spaces and let \(f : X \rightarrow Y\) be a fuzzy norm-preserving surjection satisfying \(f(0) = 0\). Then \(f\) is additive.