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This paper concerns with scalarization processes of set-valued optimization problems, whose objective space is a Hausdorff locally convex topological linear space and the preferences between the objective values are stated through set orderings. To be precise, general necessary and sufficient optimality conditions for minimal and weak minimal solutions of these optimization problems are obtained by dealing with abstract scalarization mappings that satisfy certain order preserving and order representing properties. Then these conditions are applied to well-known scalarization mappings in set optimization. This approach extends and unifies the main nonlinear scalarization results of the literature on set optimization problems with set orderings.