# FLAME-VQA: A Fuzzy Logic-Based Model for High Frame Rate Video Quality Assessment
## 4 Fuzzy Logic in User Experience Assessment
### The Model Development Process
#### 4.2.1 Fuzzification of the Scalars
Specifically, there were six different video frame rate values (24, 30, 60, 82, 98, and 120 fps), with CRF values ranging from 0 to 63, depending on the fps and the resulting bitrate. To compute the SI and TI values, we utilized the MSU Quality Measurement Tool (version 14.1) [43], calculating them for each of the 480 test sequences and then multiplying them by 1000 to enable clustering. The Gaussian-shaped membership function is preferred in fuzzy clustering algorithms, such as FCM, due to its smoothness, centeredness, and decay properties. Centering the Gaussian function at the cluster center ensures that data points closer to the center have higher membership degrees, indicating a stronger association with the cluster. The decay property enables the function to capture the gradual decrease in membership as data points move away from the center. Additionally, the Gaussian function's parameters have intuitive interpretations, making it more interpretable and facilitating the understanding of fuzzy assignments. Lastly, the mathematical tractability and efficiency of the Gaussian function simplify the optimization process during fuzzy clustering, making it computationally efficient for practical applications with complex data patterns and overlapping clusters. As we delved deeper into the performance analysis of our model and extensively experimented with various rules, membership function shapes, and configurations, we identified a specific scenario that warranted a slight modification in our approach. For the medium compression cluster associated with the video crf input variable, we observed that the standard Gauss2 function did not fully align with the underlying data distribution. To address this challenge, we made a judicious adjustment to the membership function for  
Figure 3: Membership functions of our fuzzy clusters. (**a**) Video FPS; (**b**) Video CRF; (**c**) SI; (**d**) TI. that specific cluster. We introduced a subtle alteration that resulted in a trapezoidal-like shape, with a gentle rightward inclination (Figure 3b). This tailored modification allowed the membership function to better align with the characteristics of the data points associated with that particular cluster, enabling more precise modeling of the nuances within that region of the input space. The adjustment of the function engendered a heightened membership strength for CRF values exceeding the cluster center (37.17) yet remaining below or equal to 54, specifically directing them towards the Medium compression cluster. This contrasted with the behavior observed in the High compression cluster, where the same range of CRF values exhibited comparatively lower membership. Finally, the process of fuzzification was applied to the output of the model, which represents the assessed video quality, quantified using MOS. We generated five distinct fuzzy clusters to represent the output, with each cluster center aligned to the corresponding numerical rating (Figure 4). In Table 1 we list the properties of the defined membership functions depicted in Figures 3 and