Some new operation rules and a new ranking method for interval-valued intuitionistic linguistic numbers.

An interval-valued intuitionistic linguistic set (IVILS) is introduced as an extension of both a linguistic term set and an interval-valued intuitionistic fuzzy set. However, the arithmetic operations and comparison methods of IVILS exist some limitations, which may result in information loss and distortion. To avoid this problem, the arithmetic operations are improved and a new comparison method based on a possibility degree is developed. Then, several arithmetic aggregation operators are proposed to aggregate interval-valued intuitionistic linguistic numbers. Moreover, a multi-criteria group decision-making (MCDM) approach based on the new aggregation operators is presented. Finally, the validity and effectiveness of the proposed method are confirmed by a comparable example.