This paper is concerned with multi-objective linear programming problems in which the coefficients are expressed as fuzzy numbers of triangular type. An interactive method, to enhance the weights in the weighted sum problem, is introduced.Fuzzy numbers have been used to express the lack of information existing in practice. Using the concept of α-level sets of fuzzy numbers, the corresponding deterministic α-multi-objective linear programming problem has been obtained. In order to produce the numerical weights included in the weighting sum approach, an interactive algorithm has been presented. This algorithm allows the DM to participate in the steps of finding the optimal solution. An illustrative example has been given . A numerical example is given to clarify the presented method.