Some intuitionistic trapezoidal fuzzy aggregation operators based on Einstein operations and their application in multiple attribute group decision making

Information aggregation is a key problem in decision making. The aim of this paper is to investigate information aggregation methods under intuitionistic trapezoidal fuzzy environment. Some Einstein operational laws on intuitionistic trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Then, some intuitionistic trapezoidal fuzzy aggregation operators based on Einstein operations are proposed, such as intuitionistic trapezoidal fuzzy Einstein weighted averaging operator, intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging operator, induced-intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging operator, intuitionistic trapezoidal fuzzy Einstein hybrid averaging operator, intuitionistic trapezoidal fuzzy Einstein weighted geometric operator, intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric operator, induced intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric operator and intuitionistic trapezoidal fuzzy Einstein hybrid geometric operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making in which decision information takes the form of intuitionistic trapezoidal fuzzy numbers. Finally, an illustrative example is given to demonstrate its practicality and effectiveness.