The intuitionistic linguistic (IL) variable (ILV) can express the vague and uncertain information in a better way, and the partitioned Heronian mean (PHM) operator can group attributes that have relationships with each other into one zone and the independent attributes are in different zones, so in this paper, we will propose some new PHM operators for IL information (ILI) and then apply them to multiple attribute group decision-making (MAGDM). Firstly, the some improved operational rules for ILVs are developed, which can provide a more accurate result and avoid the loss of information, then we extend the PHM operator to the IL environment and propose the intuitionistic linguistic partitioned Heronian mean (ILPHM) operator and the intuitionistic linguistic weighted partitioned Heronian mean (ILWPHM) operator, which can fully consider the advantages of the ILI and the PHM operator. Meanwhile, we discuss some desirable properties and special cases of the two operators. Further, we develop the MAGDM approach with ILI based on the developed operators. Lastly, a numerical instance is given to verify the feasibility and the superiority of the proposed method.
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