Nonlinear scalarizations in set optimization with variable ordering structures and applications

A new version of the nonlinear scalarizing function in set optimization based on variable ordering structures is proposed. Under appropriate assumptions, the properties of this function by employing set less order relations are studied. As applications, the optimal and weakly optimal solutions of set optimization problems with variable domination structures are characterized by using the above scalarizing function. Our results generalize or extend some of the existing ones in the literature.