## 3 VQA Model Design
### Membership Functions and Compact Rule Base  
The resulting membership functions for the chosen set of RoI, SF, AR, and RR values are depicted in Figure 3; the subplots also illustrate the linguistic interpretations that were assigned to the fuzzy clusters that serve as antecedents in the rule base. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Levels Tested** & **H-Statistic** & **\(p\)-Value** & **Interpretation** \\ \hline RoI & 0.50/0.60/0.70/0.80 & 11.77 & 0.0082 & RoI has a statistically significant effect (\(\alpha=0.05\)). \\ SF & 1.1/1.3/1.5 & 123.88 & 1.3 \(\times\) 10\({}^{-27}\) & SF is the dominant driver of performance. \\ AR & 0.5/0.6/0.7 & 0.00 & 1.000 & AR has no measurable impact in the \\ RR & 0.1/0.2/0.3 & 62.98 & 2.1 \(\times\) 10\({}^{-14}\) & Reject ratio significantly affects RMSE. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: One-factor Kruskal–Wallis analysis of the influence of subtractive clustering parameters (RoI, SF, AR, RR) on RMSE. Figure 3: Membership functions that describe the fuzzy clusters of the input parameters. Note that the subplot legends show linguistic meanings of the fuzzy clusters, as well as the properties of the Gaussian functions in a form (mean, st. dev. ): (**a**) video CRF; (**b**) video FPS; (**c**) video SI; (**d**) video TI. In addition, the ANFIS framework derives a set of fuzzy IF-THEN rules, wherein each rule associates a unique combination of input membership functions with a corresponding output value using a weighted average approach [10; 13]. The final rule set, presented in Table 3, maps these combinations to the predicted MOS values, encapsulating the optimized decision-making process of the model. As seen from Table 3, the model operates on seven rules, making it lightweight and less complex compared to the previous model [6], which relied on 36 rules. Furthermore, it is important to note that, since the ANFIS framework employs a Sugeno-type FIS, the output variable is generated as a weighted combination of rule consequents rather than through membership functions. The Sugeno-type FIS is particularly well-suited for VQA due to its computational efficiency and streamlined rule evaluation [14]. Unlike Mamdani systems, where each rule's fuzzy output must be aggregated and subjected to a, for instance, resource-intensive centroid defuzzification, the Sugeno framework computes each rule's crisp output via a simple linear function, as exemplified in Table 3, and then forms the final prediction as a weighted average of those rule outputs. In this study, only seven rules are evaluated per inference, compared to 36 in the previous Mamdani-based model [6]. Since each rule in a Sugeno FIS requires only membership-degree lookups and a small number of additions for the consequent's linear function, the overall inference complexity scales approximately \(O(R\cdot Q)\), with \(R\) rules and \(Q\) inputs, rather than the much heavier \(O(R\cdot U)\) integration steps demanded by [PERSON]'s centroid method (where \(U\) is the resolution of the output universe). This reduction in rule count and the use of weighted-average defuzzification translate directly into lower per-sample compute and memory overhead, making the ANFIS-VQA model more suitable for real-time monitoring of streaming services. After fuzzification and the formulation of fuzzy rules, the Sugeno-type FIS employed in the ANFIS model produces a crisp output, the predicted MOS rating, using a defuzzification process. Specifically, the fuzzy inference process is structured into five layers (Figure 4) that collectively convert raw input values into a crisp output (the predicted MOS). Note that [13] was used to mathematically describe the inference logic of the model through Equations (1)-(5). In Layer 1, each node computes the membership degree of an input using Gaussian membership functions (Figure 3), thereby mapping the raw input \(x\) to a value \(\mu(x)\) via:  
\[\mu(x)=exp\left(-\frac{(x-c)^{2}}{2\sigma^{2}}\right), \tag{1}\]