## 6 Conclusions  
The research aimed to propose an evaluation method for public service interfaces to enhance users' engagement with the interface and the efficiency of acquiring interface information. This endeavor seeks to contribute to the establishment of a sustainable digital cultural social service system, fostering cultural dissemination and preservation, and facilitating sustainable cultural development. Through an analysis of users' aesthetic preferences and cognitive principles, a mapping model between the two is formulated and utilized to calculate their correlation, thereby furnishing theoretical and methodological guidance for designers and enterprises engaged in interface design. Addressing the limitations of the original gray H-convex correlation model, which overlooks the issue of indicator weighting, this study presents an improved model, leveraging the ICRITIC method for the first time. It is demonstrated that the enhanced model offers superior accuracy and performance compared to other gray models. Consequently, this research entails both theoretical and practical innovations. The key findings of the study are outlined as follows. 1. This paper employs the enhanced gray H-convex correlation model, enabling precise identification of positive and negative correlations between interface layout aesthetics and visual cognition. The findings demonstrate that the accuracy of the enhanced model exceeds 90%. Nevertheless, the computational complexity of the model leads to a moderate increase in running time. Efforts will be directed towards addressing this limitation through further optimization in future endeavors. 2. A notable correlation exists between interface layout aesthetics and user visual cognition. Specifically, the correlations between fixation duration and fixation count are the most pronounced (0.9831 and 0.9353, respectively), which is highly consistent with the findings of [PERSON] et al. [51]. However, this study differs by explicitly calculating the degree of their correlation. Moreover, the correlation between mean pupil diameter and symmetry exhibits the highest value (0.7124), which is consistent with the findings of [PERSON] et al. [52]. Simultaneously, we found that the correlation between gaze shift frequency and order is notably strong (0.9808), while the correlation between fixation time percentage and dominance is the highest (0.9710). The inverse relationship between fixation duration, fixation count, and mean pupil diameter with interface layout aesthetics is consistent with the findings of [PERSON] et al. [53]. Notably, this study found that gaze shift frequency and gaze time percentage are positively correlated with interface layout aesthetics. These findings underscore the importance for designers to prioritize factors such as dominance, symmetry, and order of interface layout in designing interfaces for infrequently accessed public services like virtual museums. Furthermore, attention should be directed towards understanding user cognitive and physiological tendencies, as well as aesthetic inclinations, to enhance user experience and interaction efficiency. Figure 12: Comparison of model accuracy and computing time: gray correlation, gray absolute correlation, and gray H-convex correlation. 3. Nevertheless, the evaluation samples utilized in this paper exclusively encompass 2D static layout interfaces, thereby overlooking the undeniable influence of dynamic interface layout designs on user visual cognition. In forthcoming research, we intend to incorporate immersive 3D dynamic interactive interfaces as samples to undertake a comparative study of the impact of dynamic versus static interfaces on user aesthetics and cognition. Moreover, while this study predominantly centers on interface layout, it is imperative to acknowledge that interface color schemes, icons, and interaction frameworks, as well as user emotions and personalities, constitute pivotal factors influencing interface design.