## 2 Theoretical Background
### Research Motivation and Methodology  
To improve the quality of interface design while considering users' aesthetic psychology and physiological habits, this paper proposes an evaluation method for interface layout design. Given the current lack of distinction in interface types in the research, this study focuses on evaluating infrequently contacted public service interfaces, using virtual museum interfaces in various provinces of China as examples. Scholars have separately studied interface layout aesthetics and visual cognition, but there is a notable gap in research combining these two aspects. Therefore, another focus of this study is to evaluate interface quality by integrating interface layout aesthetics and visual cognitive features, elucidating their relevance. To address the aforementioned issues, we have introduced the methods applied in this study. This approach aims to provide a comprehensive evaluation methodology that can guide future interface design by aligning with both aesthetic and cognitive user needs. The gray theory is named after the color. A system with completely clear information is called a white system, a system with completely unknown information is called a black system, and a system with partially known and partially unknown information is called a gray system [34]. In this study, the aesthetic value of the interface layout scheme (calculated through relevant formulae) and the user's visual cognitive features (derived from eye movement experiments) belong to the white system, as they are known quantities. However, the mapping relationship between the two belongs to the black system, as it remains unknown and unmeasurable. Therefore, this paper employs the gray model to analyze the relationship between interface layout aesthetics and visual cognitive features. While the gray H-convex correlation model is adept at determining correlation issues, it has a defect in that it ignores the weight differences of the indicators, leading to lower accuracy in model results. To address this, an improved gray H-convex correlation model is proposed using the ICRITIC method to quantitatively study the correlation between interface layout aesthetics and visual cognitive features. (1) Gray H-convex correlation Since Professor [PERSON] proposed his correlation model [35], research on gray correlation analysis has advanced rapidly. Scholars have subsequently established a series of correlation models to further explore and refine this analytical approach, including the gray entropy correlation model [36], the gray B-type correlation model [37], and new gray absolute correlation model [38], etc. The aforementioned gray correlation algorithms have some shortcomings. For example, they are suitable only for cases of positive correlation among sequence factors and have a blind spot when processing oscillatory sequences. To address these limitations, [PERSON] et al. [18] used the principles of span and arch height to express the convexity of folds at the transverse level and proposed a gray H-convex correlation model. This model effectively quantifies the degree of correlation between the factors of the series and distinguishes between positive and negative correlations. However, despite its ability to judge negative correlation problems between indicators, it overlooks differences in the weights of the indicators. (2) ICRITIC  
The ICRITIC methodology was employed to compute the weight coefficients for every aesthetic evaluation criterion, aiming to enhance the optimization of the gray H-convex correlation mode. Traditional CRITIC approaches rely on standard deviation and correlation coefficients to assess the intensity of comparison and conflict [39; 40]. Nonetheless, variations in indicator dimensions and magnitudes pose challenges, rendering standard deviation insufficient for accurately reflecting the comparative strength among indicators. Furthermore, it is worth noting that the correlation coefficient among indicators often exhibits a negative correlation.