Existence theorems of set optimization with set-valued maps

In optimization with set-valued maps, there are two types of criteria of solutions; one is vector optimization, which is the usual one, and the other is set optimization, which is based on a natural idea and defined by this paper. The aim of the paper is to study set optimization. We consider criteria of solutions of set optimization, show some examples with respect to the criteria, introduce some type of semicontinuities for set-valued maps, and show existence theorems of solutions.