Group decision making based on linguistic intuitionistic fuzzy Yager weighted arithmetic aggregation operator of linguistic intuitionistic fuzzy numbers

In this paper, we propose two new group decision making (GDM) approaches based on the proposed linguistic intuitionistic fuzzy Yager weighted arithmetic (LIYFWA) aggregation operator (AO) of linguistic intuitionistic fuzzy numbers (LIFNs), where the proposed first GDM considers the situation that experts' weights and attributes' weights are completely known; the proposed second GDM approach considers the situation that experts' weights and attributes' weights are completely unknown. Firstly, we propose new operational laws for LIFNs based on Yager's norm, namely, the addition operation operation and the scalar multiplication operation. The proposed addition operation and the proposed scalar multiplication operation of LIFNs can conquer the drawbacks of the existing addition operation and the existing scalar multiplication operation of LIFNs. Then, based on the proposed addition operation and the proposed scalar multiplication operation of LIFNs, we propose the LIYFWA AO of LIFNs. We also prove some properties of the proposed LIFYWA AO. Finally, based on the proposed LIFYWA AO, we propose two new GDM approaches of LIFNs. The proposed GDM approaches can conquer the drawbacks of existing GDM methods, where they cannot distinguish the ranking orders of alternatives in some situations.