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This paper introduces an algorithm for researching the achievement stability set for parametric rough linear goal programming (PRLGP) issues with parameters in the achievement function and roughness in goal and system constraints. The proposed goal programing model has two types of uncertainty. We transform the PRLGP into an upper approximation model and a lower approximation model. Then, the Lexicographical goal programing method is utilized to solve such upper and lower approximation models iteratively to avoid the complexity of the attainment issue. This model has been applied as it enables the decision-maker to articulate the weights for goals however, for the sub-goals it shall be complicated as they possess the same measure. Finally, to clarify how to investigate the achievement stability set for the PRLGP, an algorithm and a numerical illustration was given.

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