An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level

In certain real decision-making situations, decision makers often feel more comfortable providing their knowledge and preferences in linguistic terms. Unbalanced linguistic term sets may be used in decision problems with preference relations. However, the lack of consistency in decision-making with linguistic preference relations can lead to inconsistent conclusions. Based on the consistency measure of unbalanced linguistic preference relations, this paper proposes an optimization-based approach to improving the consistency level of unbalanced linguistic preference relations. This consistency-improving model preserves the utmost original knowledge and preferences in the process of improving consistency. Furthermore, it guarantees that the elements in the optimal adjusted unbalanced linguistic preference relation are all simple unbalanced linguistic terms. Finally, we propose a mixed 0–1 linear programming aimed to obtain the optimum solution to the proposed consistency improving model and to demonstrate its practicability.