In recent years, the development of electric vehicles has received extensive attention. However, how to choose a suitable charging pile manufacturer for electric vehicles is a matter of concern. The selection of charging pile manufacturers involves many factors, and it is hard for decision makers (DMs) to provide accurate assessments due to the uncertainty of subjective or objective factors. As a combination of q-rung orthopair fuzzy set (q-ROFS) and dual hesitant fuzzy set (DHFS), q-rung dual hesitant fuzzy set (q-RDHFS) provides more possibilities for information expression and gives DMs greater decision-making freedom. Because of the advantages of q-RDHFS in expressing uncertain information, we propose a novel decision method to capture DMs’ hesitant information with q-rung dual hesitant fuzzy elements (q-RDHFEs) to obtain the optimal scheme. Firstly, Frank t-norm and t-conorm (FTT) is well known for its flexibility in coping with compatibility compared to traditional algebraic operation. Considering the advantages of FTT, we extend FTT to q-RDHFS and provide the definition of Frank operational rules of q-RDHFS. Subsequently, according to generalized power average (GPA) and generalized power geometric (GPG) operators, some corresponding operators based on the novel operational laws are proposed. Then, with the proposed operators, a novel multi-attribute decision-making (MADM) method under q-RDHFS environment is introduced and applied to the selection of charging pile manufacturers. Finally, compared with the existing methods, the method proposed in this paper can better handle extreme evaluation information and is more flexible in operation.