We present a fixed point approach to find the whole solution set of a set-valued optimization problem though a parametric problem, in which the height of the level set of the objective function is regarded as the parameter. First, the solution concept based on the vector approach is considered in this method. Then, we propose another solution concept which additionally takes the maximal part of the set into consideration and compare it with the solution concept based on the set approach. The fixed point approach is also extended to set-valued optimization with respect to this solution concept. Finally, a special case of this theory is investigated particularly, for which the new solution concept actually provides a vectorization.

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