## 3 VQA Model Design
### Surface Visualisation and Sensitivity Analysis  
Based on the process described above, as well as the membership functions shown in Figure 3 and the fuzzy rule set listed in Table 3, insight can be gained into how the input parameters collectively influence the output. Figure 5 presents a series of surface subplots that illustrate the relationship between all possible pairs of input parameters and the predicted MOS rating, revealing the nonlinear interactions captured by the neuro-fuzzy inference system. Figure 5: The relationship between pairs of input parameters and the output (Predicted MOS): (**a**) video FPS and CRF; (**b**) video FPS and SI; (**c**) video FPS and TI; (**d**) video CRF and SI; (**e**) video CRF and TI; (**f**) video SI and TI. The visualizations demonstrate that the interplay among variables (specifically, compression rate expressed via CRF levels, frame rate, spatial information, and temporal information) is highly complex. For example, the effect of compression on perceived quality can vary dramatically depending on the frame rate (Figure 5a), the level of spatial detail present in the video (Figure 5d), or the level of motion of the screen (Figure 5e). In addition, the combined impact of spatial and temporal information on user perception is not simply additive, but rather synergistic, resulting in subtle distortions that are challenging to predict with traditional models (Figure 5f). Building on these insights, a targeted sensitivity analysis was conducted to quantify how each input alone drives the MOS prediction under varying context levels of the other three parameters. In Figure 6, four subplots (a-d) show the predicted MOS as one input sweeps from its minimum to maximum value, while the remaining inputs are fixed at low, medium, or high settings. Figure 6: Sensitivity analysis of the ANFIS-VQA model. Three input variables remained fixed while varying: (**a**) VideoCRF; (**b**) VideoFPS; (**c**) VideoSI; (**d**) VideoTI. As seen in Figure 6a, an increase in VideoCRF leads to a sharp decline in MOS, most dramatically when frame rate, spatial information, and temporal information are all low. This behavior aligns with expectations since heavily compressed video with fast scene changes and dynamic content will suffer more perceptible artifacts. Under high-quality settings, the model remains somewhat robust yet still exhibits quality loss at extreme compression, reflecting its sensitivity to subtle distortions. Figure 6b shows that as the frame rate rises, the MOS prediction increases in a nonlinear manner, especially when other parameters are low, because fluid motion at high FPS mitigates the impact of spatial or temporal shortcomings; improvements taper off beyond around 100 fps, indicating a saturation of the smoothness benefit. In Figure 6c, boosting spatial information yields a consistent uplift in MOS regardless of compression, frame rate, or motion complexity, demonstrating that richer scene detail uniformly enhances perceived quality. Finally, Figure 6d reveals that temporal information has a mildly nonmonotonic effect in low-quality contexts. Predicted MOS improves at moderate motion levels, then plateaus or slightly decreases at very high motion, reflecting the model's recognition that excessive motion complexity can overwhelm viewers, whereas in high-quality scenarios, increased temporal detail produces a steady gain in perceived quality. This complexity underscores the fact that user perception of HFR video quality is influenced by multiple interdependent factors and that a sophisticated modeling approach, like the neuro-fuzzy system, is required to capture these multidimensional relationships. Ultimately, the surface plots (Figure 5) and the sensitivity analysis (Figure 6) not only illustrate the direct effects of individual inputs but also highlight how their interactions drive the overall quality assessment, emphasizing the necessity for a robust, adaptive model in real-world multimedia applications.