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In this paper, some new nonlinear scalarization functions are introduced and some of their properties are investigated. Using these functions and the polar cone, we characterize set optimal solutions of set optimization problems. Also, some relationships between the cone-convexity (resp. cone-quasiconvexity) of a set-valued map and the convexity (resp. quasiconvexity) of its scalarized versions are established. 相似文献