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This study investigates a multi-objective minimum cost flow with probabilistic objective function coefficients (Poss- MOMCF). Under using the cut set of the possibilistic variables, the Poss-MOMCF problem is converted into the corresponding ( -MOMCF) and hence into the ( -MOMCF) problem. A necessary and sufficient condition for investigating the possibly optimal solution is established. A fuzzy goal programming approach is applied to obtain the parametric optimal compromise solution. The stability set of the first kid under the concept of possibly optimal solution is characterized and analyzed without differentiability. Finally, a numerical example is given in the sake of the paper to clarify the methodology.
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