The advanced approach to cross-domain sentiment recognition plays a crucial role in enhancing the robustness and adaptability of sentiment analysis (SA) models across domains with varying linguistic patterns and vocabularies. An intelligent decision-making model is applied to evaluate the authenticity of preferences under different conflicting criteria and with insufficient expert information. This manuscript presents a novel approach, the picture fuzzy rough set (PFRS), to address uncertainty and vagueness in human judgments and during integration. Besides the theoretical concepts of picture fuzzy rough (PFR) information, some feasible operations of the Frank t-norm and t-conorm are also formulated within the PFR framework. We developed a family of robust mathematical methodologies of Frank aggregation operators, namely picture fuzzy rough Frank weighted average (PFRFWA) and picture fuzzy rough Frank weighted geometric (PFRFWG) operators. To highlight the validation and compatibility of derived approaches, some special cases and dominant properties are also discussed. To address complexities in real-life applications and numerical examples, an intelligent decision-making approach is established based on the evaluation distance from the average solution (EDAS) method and the PFR framework. Some deep fusion approaches are evaluated using decision-making methodologies with numerical examples. Sensitivity analysis demonstrates the robustness and superiority of the derived mathematical approaches. Finally, a summary of the article is provided at the end.