<abstract><p>The need for multi-attribute decision-making brings more and more complexity, and this type of decision-making extends to an ever wider range of areas of life. A recent model that captures many components of decision-making frameworks is the complex $ q $-rung picture fuzzy set (C$ q $-RPFS), a generalization of complex fuzzy sets and $ q $-rung picture fuzzy sets. From a different standpoint, linguistic terms are very useful to evaluate qualitative information without specialized knowledge. Inspired by the ease of use of the linguistic evaluations by means of 2-tuple linguistic term sets, and the broad scope of applications of C$ q $-RPFSs, in this paper we introduce the novel structure called 2-tuple linguistic complex $ q $-rung picture fuzzy sets (2TLC$ q $-RPFSs). We argue that this model prevails to represent the two-dimensional information over the boundary of C$ q $-RPFSs, thanks to the additional features of 2-tuple linguistic terms. Subsequently, some 2TLC$ q $-RPF aggregation operators are proposed. Fundamental cases include the 2TLC$ q $-RPF weighted averaging/geometric operators. Other sophisticated aggregation operators that we propose are based on the Hamacher operator. In addition, we investigate some essential properties of the new operators. These tools are the building blocks of a multi-attribute decision making strategy for problems posed in the 2TLC$ q $-RPFS setting. Furthermore, a numerical instance that selects an optimal machine is given to guarantee the applicability and effectiveness of the proposed approach. Finally, we conduct a comparison with other existing approaches.</p></abstract>