## 5 Fuzzy Model  
To analyze and validate the SUS and UEQ-S results in a way that adequately captures the variability and trends in user responses, the fuzzy logic model was used in this study. To implement this model, we used Python [65; 66] with the scikit-fuzzy library, in which we created antecedent and consequent objects for the variables, defined the membership functions with methods such as trim (triangular function) or trapmf (trapezoidal function), configured the control system with the inference rules, and, finally, executed the model to obtain de-fuzzy results that provide the probability of recommendation and the quality of the user's experience in clear values. The following are the steps. 1. Definition of Variables and Fuzzy Sets The variables that would be part of the fuzzy model, in the context of SUS and UEQ-S, were defined. Each of these variables was modeled as a fuzzy set with degrees of membership ranging from 0 to 1. We have the following: Input Variables (SUS- and UEQ-S-based). * Ease of use (SUS): \(F(x)\) [0, 101, 1]
* Satisfaction (UEQ-S): \(S(x)\) [\(-3,4,1\)]
* Efficiency (average task time): \(E(x)\) [0, 601, 1]  
Each variable is associated with a membership function, which indicates the degree to which a specific value belongs to the fuzzy set. These functions are represented as  
\[\mu_{F}(x):x \rightarrow[0,1]\] \[\mu_{S}(x):x \rightarrow[0,1]\] \[\mu_{E}(x):x \rightarrow[0,1]\]  
where \(\mu_{F}(x),\ \mu_{S}(x),\ \mu_{E}(x)\) are the membership functions for Ease of Use, Satisfaction and Efficiency, respectively, and x is the specific value of each variable. Output Variables (Objective of the Analysis)  
* Probability of recommendation: \(P(y)\) [0, 101, 1]
* Overall quality of user experience: \(Q(y)\) [0, 101, 1]  
Here, \(\mu_{P}(y),\ \mu_{Q}(y)\) represent the membership functions for the probability of recommendation and overall quality of user experience, respectively, and y is the specific value of each output variable. For the input variable \"ease of use\", values range from 0 to 100, with increments of 1. This means that ease of use can be rated on a scale of 0 to 100, where 0 represents a very low ease of use and 100 represents a very high ease of use. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Pragmatic Quality**} & \multicolumn{2}{c}{**Hedonic Quality**} \\
**Items** & **Correlation** & **Items** & **Correlation** \\ \hline
1.2 & 0.35 & 5.6 & 0.69 \\
1.3 & 0.68 & 5.7 & 0.23 \\
1.4 & 0.52 & 5.8 & 0.53 \\
2.3 & 0.53 & 6.7 & 0.47 \\
2.4 & 0.79 & 6.8 & 0.59 \\
3.4 & 0.53 & 7.8 & 0.54 \\
**Average** & 0.57 & **Average** & 0.51 \\
**Alpha** & **0.84** & **Alpha** & **0.81** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Item correlations by scale and Cronbach's alpha coefficient. For the input variable \"satisfaction\", values range from \(-3\) to \(3\), with increments of \(1\). This indicates that satisfaction can be rated on a scale of \(-3\) to \(3\), where negative values represent dissatisfaction, \(0\) represents neutrality, and positive values represent satisfaction. For the input variable \"efficiency\", values range from \(0\) to \(600\), with increments of \(1\). This suggests that efficiency can be measured on a scale of \(0\) to \(600\), where higher values indicate greater efficiency. For the output variables \"probability of recommendation\" and \"UX quality\", the values also range from \(0\) to \(100\), with increments of \(1\). This means that both the likelihood of recommendation and the quality of the user experience can be evaluated on a scale from \(0\) to \(100\), where higher values indicate a higher likelihood of recommendation or a higher quality of the user experience. 2. Creating Membership Functions  
For each input variable, we define or create membership functions that describe how the degrees of membership are assigned to the values of the variable, and we use mathematical functions that represent the descriptions, as shown in Figure 10 and Table 11.