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Linguistic intuitionistic fuzzy numbers (LIFNs) is a new concept in describing the intuitionistic fuzzy information, which membership and non-membership are expressed by linguistic terms, so it can more easily express the fuzzy information, and some research results on LIFNs have been achieved. However, in the existing researches, some linguistic intuitionistic fuzzy aggregation operators are based on the traditional operational rules, and they have some drawbacks for multi-attribute decision making (MADM) in the practical application. In order to overcome these problems, in this paper, we proposed some improved operational rules based on LIFNs and verified their some properties. Then we developed some aggregation operators to fuse the decision information represented by LIFNs, including the improved linguistic intuitionistic fuzzy weighted averaging (ILIFWA) operator and the improved linguistic …