An inexact approach is proposed to solve objective/resource type of fuzzy linear programming problems. Instead of finding an exact optimal solution, this approach uses a recommended genetic algorithm with mutation along the weighted gradient direction to find a family of inexact solutions with acceptable membership degree. Then, by means of the human-computer interaction, the solution preferred by the decision-maker can be achieved by a convex combination of the solutions selected from the family. The numerical analysis has shown that the more satisfactory results can be achieved by this new approach.