LAUSR

Abstract We introduce the concept of null set in the hyperspace that is consisting of all nonempty subsets of a given normed space. Based on the concepts of null set and convex cone, we can define two partial orderings according to the algebraic difference and Hukuhara difference between any two elements in the hyperspace, which will be used to define the solution concepts of set optimization problems. On the other hand, we transform set optimization problems into a conventional vector optimization problem. Under these settings, we can apply the technique of scalarization to solve this transformed vector optimization problem. Finally, we show that the optimal solution of scalarized problem is also the optimal solution of original set optimization problem.