In this paper we propose a method to solve a linear programming problem involving fuzzy parameters whose possibility distributions are given by fuzzy numbers. To address the above problem we have used a preference relationship of fuzzy numbers that leads us to a solving method that produces the so-called $\alpha$-degree feasible solutions. It must be pointed out that the final solution of the problem depends critically on this degree of feasibility, which is in conflict with the optimal value of the objective function. Then DM faces a bi-objective problem that we will solve through a Compromise Programming approach, whose solution lets the Decision-Maker express his own preferences about feasibility versus optimality. Our proposed method will be illustrated by a numerical example