In this paper, we study a scalarization function and introduce well-posedness notions for set optimization problems. Some scalarization results are given for the sets of weak $ m $-minimal solutions and $ m $-minimal solutions for set optimization problems. Furthermore, we introduce novel concepts of well-posedness specifically tailored for the set optimization problem. We establish connections among three distinct types of well-posedness and explore the relationships that exist between the well-posedness of set optimization problems and that of scalar optimization problems. [ABSTRACT FROM AUTHOR]

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