Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators called the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging(I-IIULHSA) operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric(I-IIULHSG) operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure,we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ–Shapley averaging(I-IIULHλSA) operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ–Shapley geometric(I-IIULHλSG) operator. Moreover,an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.