Linear programming is the most frequently applied operations research technique. In linear programming models, the coefficients are usually expressed in definite terms. But in many real-world models, these coefficients are uncertain. Therefore, it is necessary to apply analyzes other than ordinary ones. In this paper, an interval linear programming model with fuzzy constraints is considered and new concepts of α ̅ -feasibility and α ̅–efficiency of solutions for fuzzy mathematical programming problems are used, where α ̅ is a vector of distinct satisfaction degrees. One of the most interesting models of the linear programming with fuzzy constraints named the flexible linear programming problem (FFLP) that used in this paper. By use of mentioned concepts, we proposed a two-phase approach to solve FFLP. In the first phase, the interval linear programming converted to two crisp sub-problem and then in phase II by simplifying the problem into two sub-problems with fuzzy constraints, two sub-problems with a parametric approach are solved.
