# 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
Subsequently, we decided to refine our approach by introducing an additional cluster for each input variable, resulting in a total of three clusters for each. This adjustment was motivated by our recognition that a more detailed representation of the data through increased cluster granularity could yield more accurate and insightful quality assessments. This approach allowed us to iteratively adjust the cluster centers based on the distribution of data points, resulting in a clustering configuration that was tailored to the inherent characteristics of the dataset. By taking this approach, we aimed to strike a balance between capturing the underlying data structure and avoiding overfitting, thereby enhancing the generalization capabilities of the model. The resulting clusters and their respective centers, for the dataset discussed in Section 3 and used for the model development, are depicted in Figure 2.  
In Figure 2 subplots, each data point represents the quality rating given by one test subject to one video, and the color codes indicate the membership of each point to a specific fuzzy cluster. Since the fuzzy rule-based system operates with linguistic variables to produce outcomes, we have named the derived clusters as shown in the figure captions. Furthermore, each subplot corresponds to one input variable of our model, and the number of clusters on the subplots represents the number of states a specific input can be in. For instance, video fps can be in three states: low, medium, and high video frame rate (Figure 2a). The figure also shows that we used subjective ratings of video quality to fuzzify scalar values of the input parameters, which can be observed from the \(y\)-axes. We discussed in Section 3.2 that the dataset utilized for this study adopted a widely recognized user rating scale, consisting of the following ratings: 0 = Bad, 1 = Poor, 2 = Fair, 3 = Good, and 4 = Excellent. To maintain consistency with the approach followed in [9], where the ratings were multiplied by a factor of 10, we adopted the same methodology. In addition, before clustering, we multiplied the SI and TI metrics of each video sequence by a factor of 1000. This helped execute the FCM algorithm; otherwise, the algorithm returned the error, since the values were too small to determine the cluster boundaries. The figure also underscores the dispersion of data points encompassing all MOS rating categories, thereby posing a challenge in elucidating the precise correlation between the inputs and the model output. It is important to recall that the clustering was executed on the training set, which contained 80% of the original data. After completing the FCM process and obtaining the coordinates of the cluster centers, we created the membership functions for each cluster. The membership function serves as a quantitative indicator of the extent to which individual data points are associated with a particular cluster. To accomplish this, we employ Gaussian combination membership functions (Gauss2) for each cluster. The Gauss2 function is characterized by its utilization of two distinct Gaussian membership functions, a feature that facilitates fine-tuning of both the mean and sigma values, allowing for a more accurate representation of the data's clustering behavior. The sigma of a function has to be defined so that the function tail reaches \(y=0\) at the \(x\) coordinate of the adjacent cluster center. The obtained membership functions for each cluster are depicted in Figure 3.  
Figure 2: Results of the FCM clustering. For each input variable, three fuzzy clusters were used. (**a**) Video FPS cluster names: low, medium, and high frame rate; (**b**) Video CRF cluster names: low, medium, and high compression; (**c**) SI cluster names: low, medium, and high complexity; (**d**) TI cluster names: low, medium, and high frame diversity. As in Figure 2, the \(x\)-axes values in Figure 3 correspond with the properties of the video sequences discussed in Section 3.1.