Multiattribute group decision making based on Aczel–Alsina linguistic intuitionistic fuzzy weighted averaging operator of linguistic intuitionistic fuzzy environment

In this paper, we present a novel approach for multiattribute group decision making (MAGDM) under linguistic intuitionistic fuzzy (LIF) environment based on the proposed LIF Aczel–Alsina weighted averaging (LIFAAWA) aggregation operator (AO) and LIF Aczel–Alsina ordered weighted averaging (LIFAAOWA) AO of LIF numbers (LIFNs). Firstly, we propose several new operations for LIFNs based on Aczel–Alsina’s norm, namely, addition operation, multiplication operation, scalar multiplication operation and scalar power operation. Then, based on the proposed operations of LIFNs, we propose the LIFAAWA AO and LIFWAAOWA AO of LIFNs. We also prove some properties of the proposed LIFAAWA AO and LIFWAAOWA AO. After that, based on the proposed LIFAAWA AO and LIFWAAOWA AO, we propose a novel MAGDM approach in the LIF environment. Finally, we solve some numerical MAGDM examples by using the proposed MAGDM approach and compare the ranking orders (ROs) obtained by the proposed MAGDM approach with the ROs obtained by the existing MAGDM approaches. The proposed MAGDM approach can overcome the drawbacks of existing MAGDM approaches, where existing MAGDM approaches cannot distinguish the ROs of alternatives in some cases. The proposed MAGDM approach provides us a very useful tool to deal with MAGDM problems under the LIF environment.