In daily life, when conventional sets are insufficient in handling problems with multi-criterion, we use trapezoidal fuzzy multi-sets to solve decision-making problems in a lot of areas. Therefore, we introduce power aggregation operators on trapezoidal fuzzy multi-numbers as a novel way. By doing this, we aimed to introduce new operators on trapezoidal fuzzy multi-numbers which allow argument values to support each other in the aggregation process. Then, we described the properties of the operators and gave a formulation for the support function that is used in the operators. Moreover, we introduced two algorithms to solve multiple attribute group decision-making problems given with trapezoidal fuzzy multi-numbers. Lastly, we applied the introduced algorithms to a zero-waste problem to show the usage of the operators.