We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973,and V¨ais¨al¨a, 2003, we provide the following generalized version of theMazur-Ulam theorem in the fuzzy context: let ���, ��� be fuzzynormed spaces and let ��� : ��� → ��� be a fuzzy norm-preserving surjection satisfying ���(0) = 0. Then ��� is additive.
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