In this paper, a novel multiple-attribute decision-making method based on a set of Archimedean power Maclaurin symmetric mean operators of picture fuzzy numbers is proposed. The Maclaurin symmetric mean operator, power average operator, and operational rules based on Archimedean T-norm and T-conorm are introduced into picture fuzzy environment to construct the aggregation operators. The formal definitions of the aggregation operators are presented. Their general and specific expressions are established. The properties and special cases of the aggregation operators are, respectively, explored and discussed. Using the presented aggregation operators, a method for solving the multiple-attribute decision-making problems based on picture fuzzy numbers is designed. The method is illustrated through example and experiments and validated by comparisons. The results of the comparisons show that the proposed method is feasible and effective that can provide the generality and flexibility in aggregation of values of attributes and consideration of interactions among attributes and the capability to lower the negative effect of biased attribute values on the result of aggregation.