Cone convexity of measured set vector functions and vector optimization

With the absence of a linear structure on a σ-algebra of sets, an accepted concept of convexity on it is defined through Morris sequences. Some known results on such a convexity for scalar valued set functions are generalized to cone convexity of vector valued measured set functions. Finally these notions are exploited in a study of vector optimization involving the latter functions, a study in which cone-optimal and proper cone-optimal solutions are characterized in a duality setting.