%0 Journal Article %T Variational Principles of Fuzzy Mappings and Its Applications %J - %D 2017 %X In this paper, we firstly discuss the basic properties of the sub differential of fuzzy mapping and get some related conclusions. Secondly, we establish a variational principle of fuzzy mapping by establishing the concept of gauge fuzzy mapping. Then we prove the approximation sun rule of fuzzy mapping in sub-differential as the application of that principles. %K Fuzzy Mapping %K Sub-differential %K Gauge Mapping %K Variational Principle %K Approximation Sun Rule %U http://www.sciencepublishinggroup.com/journal/paperinfo?journalid=149&doi=10.11648/j.sjams.20170504.13