A multicriteria group decision-making method based on AIVIFSs, Z-numbers, and trapezium clouds

Abstract

Abstract Multicriteria group decision-making (MCGDM), with the strong uncertainty and randomness, has always been a hotspot in the world. The chief purpose of the paper is to address the problem with Atanassov’s interval-valued intuitionistic fuzzy sets (AIVIFSs), Z-numbers, and trapezium clouds. First, some related concepts and former operators of AIVIFSs, Z-numbers, and trapezium clouds are reviewed, meanwhile, AIVIFSs and Z-numbers are synthesized to come up with a novel linguistic expression. Then, Z-trapezium-trapezium cloud (ZTTC) is proposed to quantify the linguistic evaluation information to avoid excessive computation caused by traditional methods. Later, a new approach of calculating the objective weight vector is presented based on entropy weight method (EWM). To take the huge advantages of technique for order preference by similarity to ideal solution (TOPSIS) method in ranking, 2-norm in mathematical theory is applied to derive a way of calculating the distance between different ZTTCs. Finally, an example about the grade assessment of coronavirus Disease 2019 (COVID-19) is given. For further confirming the validity and feasibility, sensitivity analysis and comparison with other methods are conducted.