A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces - J. J. Font; J. Galindo; S. Macario; M. Sanchis (Abstract and Applied Analysis)
We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, 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→Y be a fuzzy norm-preserving surjection satisfying f(0)=0. Then f is additive.