The recently proposed q-rung dual hesitant fuzzy sets ( q-RDHFSs) not only deal with decision makers’ (DMs’) hesitancy and uncertainty when evaluating the performance of alternatives, but also give them great liberty to express their assessment information comprehensively. This paper aims to propose a new multiple attribute decision-making (MADM) method where DMs’ evaluative values are in form of q-rung dual hesitant fuzzy elements ( q-RDHFEs). Firstly, we extend the powerful Schweizer-Sklar q-norm and t-conorm (SSTT) to q-RDHFSs and propose novel operational rules of q-RDHFEs. The prominent advantage of the proposed operations is that they have important parameters q and r, making the information fusion procedure more flexible. Secondly, to effectively cope with the interrelationship among attributes, we extend the Hamy mean (HM) to q-RDHFSs and based on the newly developed operations, we propose the q-rung dual hesitant fuzzy Schweizer-Sklar Hamy mean ( q-RDHFSSHM) operator, and the q-rung dual hesitant fuzzy Schweizer-Sklar weighted Hamy mean ( q-RDHFSSWHM) operator. The properties of the proposed operators, such as idempotency, boundedness and monotonicity are discussed in detail. Third, we propose a new MADM method based on the q-RDHFSSWHM operator and give the main steps of the algorithm. Finally, the effectiveness, flexibility and advantages of the proposed method are discussed through numerical examples.