Some uncertain generalized Shapley aggregation operators for multi-attribute group decision making

This paper studies some uncertain generalized aggregation operators based on the Shapley function, two of which are named the uncertain induced generalized Shapley averaging (UIGSA) operator and the uncertain induced generalized hybrid Shapley averaging (UIGHSA) operator. These two operators consider the interactive characteristics between elements and that of their ordered positions. Meanwhile, some important cases and desirable properties are studied. To simplify the complexity of solving a fuzzy measure, the uncertain induced generalized λ -Shapley averaging (UIG λ SA) operator and the uncertain induced generalized hybrid λ -Shapley averaging (UIGH λ SA) operator based on λ -fuzzy measures are presented. Finally, two new approaches to uncertain multi-attribute group decision making are developed, and a numerical example is provided to illustrate the proposed procedures.