Abstract
We introducefuzzy norm-preservingmaps, 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: letX,Ybe fuzzy normed spaces and letf:X→Ybe a fuzzy norm-preserving surjection satisfyingf(0)=0. Thenfis additive.
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