Trapezoidal picture fuzzy aggregation operators based on Einstein operations and its application to multi-attribute decision making problem.

In this paper, the concept and operational laws of trapezoidal picture fuzzy numbers are first introduced. Then, the trapezoidal picture fuzzy Einstein weighted geometric aggregate operator and trapezoidal picture fuzzy Einstein ordered weighted geometric aggregate operator are developed by using Einstein t-norms and t-conorms. Various characteristics of the proposed operators are explored in detail. Then a multi attribute decision-making problems under picture fuzzy environment is solved using the proposed operators. Finally, a numerical example is presented to illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]