Two-sided interval linear systems contain variables on both sides of equations or inequalities. We propose six types of solutions (weak, strong, tolerance, control, left-localized and right-localized solutions) to the system of equations together with four types of solutions (weak, strong, tolerance and control solutions) to the system of inequalities. We prove the necessary and sufficient conditions for checking their solvabilities in the form of systems of linear inequalities depending on the sign of variables. As a result, an interval linear programming problem with nonnegative variables and two-sided interval linear constraints can be solved by a standard linear programming approach.

双面区间线性系统的方程式或不等式两边都包含变量。我们提出方程系统的六种类型的解决方案（弱，强，公差，控制，左局部和右局部解）以及不等式系统的四种类型的解决方案（弱，强，公差和控制方程） 。我们证明了以线性不等式形式（取决于变量的符号）检查其可解性的必要和充分条件。结果，可以通过标准线性规划方法来解决具有非负变量和两侧间隔线性约束的区间线性规划问题。