Interactive fuzzy goal programming approach for solving possibilistic multi-objective minimum cost flow problems

In this study, a multi-objective minimal cost flow with possibilistic objective function coefficients (Poss-MOMCF) is studied. Under using the α-cut set of the possibilistic variables, the Poss-MOMCF problem is converted into the corresponding (α-MOMCF) and hence into the (P-MOMCF) problem. A necessary and sufficient condition for investigating the α-possibly optimal solution is established. The α-parametric optimal compromise solution is obtained via an interactive fuzzy goal programming approach. The stability set of the first kind under the concept of α-possibly optimal solution is characterised and analysed without differentiability. The methodology is finally illustrated using a numerical example for the sake of the study.