A note on the generalized difference and the generalized differentiability

This note reveals that the assertion in Stefanini (2008) [2] that the generalized difference between two fuzzy numbers is always a fuzzy number is incorrect. As a consequence, the theorem of existence of the generalized differentiability in Bede and Stefanini (2013) [7] is also incorrect. We propose a modification in the definition of the generalized difference in order to assure the mentioned results.