Fenchel duality for convex set functions

In this paper, we study Fenchel duality for convex set functions. We dene convex set functions in a simple way. We introduce Fenchel conjugate and investigate Fenchel duality in terms of convex
analysis on an embedding normed space of compact convex subsets. We compare our convex set functions with previous ones. In addition, we introduce robust approach for the uncertain problem as an application.