Treffer: SOLUTION OF A MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM HAVING ROUGH INTERVAL COEFFICIENTS USING ZERO-SUM GAME

In this paper, a set of compromise solutions is found for the multi-objective linear programming with rough interval coefficients (MOLPRIC) problem by proposing a two-phased algorithm. In the first phase, the MOLPRIC problem is separated into single-objective LPRIC problems considering the number of objective functions, and the rough optimal solution of each LPRIC problem is found. In the second phase, a zero-sum game is applied to find the rough optimal solution. Generally, the weighted sum method is used for determining the trade-off weights between the objective functions. However, it is quite inapplicable when the number of objective functions increases. Thus, the proposed algorithm has an advantage such that it provides an easy implementation for the MOLPRIC problems having more than two objective functions. With this motivation, applying a zero-sum game among the distinct objective values yields different compromise solutions.