Providing a Method for Solving Interval Linear Multi-Objective Problems Based on the Goal Programming Approach

Most research has focused on multi-objective issues in its definitive form, with decision-making coefficients and variables assumed to be objective and constraint functions. In fact, due to inaccurate and ambiguous information, it is difficult to accurately identify the values of the coefficients and variables. Interval arithmetic is appropriate for describing and solving uncertainty and inaccuracy in these decision-making problems. One of the important methods proposed for solving multi-objective interval problems is the best-worst-case method proposed by Tang. One of the major drawbacks of this method is the possibility of generating infeasible answers. Therefore, this paper develops a method for solving multi-objective linear programming problem. The proposed approach in this paper is to use the goal programming method to solve such problems. In this paper, a new algorithm for solving such problems is presented which in addition to reducing the complexity of solving uncertain problems by fuzzy methods, avoids high computation even if the objectives are increased. The performance of the proposed method has been tested in various numerical examples. The proposed method reduces the likelihood of creating infeasible and inefficient answers by considering possible bounds for objectives and constraints.