As a useful tool to deal with linguistic information, the interval 2-tuple linguistic representation model has been applied successfully to many group decision-making problems. However, the ranking methods to compare the interval 2-tuples exist some limitations, which may lead to information loss and even a wrong decision. To avoid this problem, a novel ranking method is developed to improve the decision accuracy. Moreover, a method based on the interval 2-tuple is presented to solve the interval-valued intuitionistic linguistic multi-criteria decision-making (MCDM) problems. Firstly, the certainty interval of an interval-valued intuitionistic linguistic number (IVILN) is defined to convert an IVILN into an interval 2-tuple. Then, an interval 2-tuple weighted arithmetic averaging (IT-WAA) operator and an interval 2-tuple ordered weighted arithmetic averaging (IT-OWA) operator are utilized to aggregate the decision information. Based on the proposed ranking method, the ranking results and the best option can be obtained. Finally, an illustrative example is provided to verify the proposed method, which is then compared to some existing approaches.
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