<p>Decision-making (DM) problems in real-world scenarios often entail ambiguity, uncertainty, and attribute prioritization, which conventional crisp or fuzzy models fail to address adequately. Intuitionistic fuzzy rough sets (IFRSs) integrate intuitionistic fuzzy sets (IFSs) with rough sets (RSs) to address uncertainty. In contrast, the Schweizer-Sklar (SS) t-norm (TN) and t-conorm (TcN) provide a flexible, parametric approach for fusing uncertain information. In this article, we offer a novel class of prioritized aggregation operators based on SS TN and TcN for IFRSs, namely intuitionistic fuzzy rough SS prioritize averaging (IFRSSPA), intuitionistic fuzzy rough SS prioritize geometric (IFRSSPG), intuitionistic fuzzy rough SS prioritized weight averaging (IFRSSPWA), and intuitionistic fuzzy rough SS prioritized weight geometric (IFRSSPWG) operators. The proposed operators differ from conventional aggregation operators (AOs) that depend on algebraic TNs and TcNs by utilizing the parametric flexibility of SS TNs and TcNs. This approach enables configurable levels of information fusion and enhanced regulation of uncertainty modelling. We investigate several core mathematical features of these operators in detail, including idempotency, monotonicity, and boundedness. A novel multi-attribute decision-making (MADM) approach is then established based on these operators. To demonstrate its practical utility, we employed the technique for customer satisfaction analysis in e-commerce, where subjective and uncertain data play a crucial role. A comparative investigation with prevailing approaches and a sensitivity analysis regarding the SS parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation> reveal the superiority, accuracy, and ranking stability of the recommended approach. These findings suggest that SS-based prioritized operators offer a powerful and versatile tool for solving complex MADM issues under uncertainty.</p>