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Linguistic variables (LVs) provide a reliable expression of cognitive information. By inheriting the advantages of LVs, we can express uncertain and incomplete cognitive information in multiple attribute decision-making (MADM), and they do so better than existing methods. In the decision-making process, we can consider decision experts’ (DEs’) bounded rationality, such as cognition toward loss caused by the DEs’ cognitive limitations during the decision process. Therefore, it is necessary to propose a novel cognitive decision approach to handle MADM problems in which the cognitive information is expressed by LVs. In this paper, we employ LVs to represent uncertain and hesitant cognitive information. Then, we propose a mathematical programming approach to solve the MADM problems where attributes or cognitive preferences are not independent. Moreover, the validity and superiority of the presented approach are verified by dealing with a practical problem.