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This work is concerned with providing solution concepts and methods for solving set optimization problems without convexity assumptions. A special focus is put on set relations, as these are crucial ingredients in the so-called set approach. Generalized set relations are introduced and characterized by means of nonlinear functionals. In addition, variable domination structures as well as approximate solution concepts are introduced and studied. For these concepts, solution procedures by meansdoi:10.25673/35671 fatcat:vxjucjl7andn7ngsigxoq4zhuq