Scalarizations for a set optimization problem using generalized oriented distance function

The aim of this paper is to establish scalarizations for minimal and weak minimal solutions of a set optimization problem using generalized oriented distance function introduced by Crespi et al. (Math Methods Oper Res 63:87-106, 2006). The solution concepts are based on a partial set order relation on the family of nonempty bounded sets proposed by Karaman et al. (Positivity 22:783-802, 2018). Finally, we also provide existence results for minimal solutions and sufficient conditions for the solution sets to be closed.