<p>In this research, linear programming problems in a rough interval environment are investigated. Rough intervals are commonly used in optimization because they provide greater flexibility in modeling and are effective at handling uncertainty. They describe uncertainty using two parts: lower approximation interval, which defines the range of surely values, and the upper approximation interval, which defines the range of possibly values. This paper presents the concepts of surely and possibly feasible solutions in rough interval linear programming problems. To determine the ranges of surely and possibly optimal solution spaces, four linear programming problems are formulated. In addition, new results are presented to guarantee that the proposed solution spaces are feasible. Several numerical examples are presented to illustrate the new results and compare them with existing methods. To address the validation, the methodology is tested using Monte Carlo simulation and evaluated through coverage rate and validity rate indicators. A comparative analysis demonstrates that our approach not only ensures feasibility but also provides interval solutions for decision variables that previous models could not obtain. Additionally, a transportation problem is analyzed to demonstrate the practical applicability of the proposed method. Unlike existing approaches, the proposed method yields rough interval solutions that encompass a broader range of values and provide greater flexibility for decision-making.</p>