Abstract
This paper deals with the multiobjective minimum cost flow (F-MOMCF) with fuzzy penalty characterized by trapezoidal fuzzy numbers. Through the use of alpha-cut, the F-MOMCF problem is transformed into the alpha-MOMCF problem. The alpha-MOMCF problem can be solved using an interactive approach combined with the weighting Tchebycheff problem. The advantages of this method are that it elicits information from the decision maker (DM) to modify the given constraint set, it gives the optimum penalty, and the effort required for obtaining the solution is reduced. The stability set of the first kind related to the alpha-best compromise solution is determined. A numerical example is given for illustration and to check the validity of the approach.