%0 Journal Article %T A study on the differential and sub-differential of fuzzy mapping and its application problem %A Bao, Yu-E %A Li, Jin-Jun %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 1 %@ ISSN 2008-1901 %F Bao2017 %X In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about the concept. At last, we study the relationships between sub-differential of fuzzy mapping and differential of convex fuzzy mappings. Moreover, a sufficient condition that a class of fuzzy mapping have convex extension is gained. %9 journal article %R 10.22436/jnsa.010.01.01 %U http://dx.doi.org/10.22436/jnsa.010.01.01 %P 1--17