## 3 Materials and Methods
### Instruments
#### 3.2.3 Fuzzy Logic  
This is a mathematical tool that allows reasoning with imprecise or vague information, using partial truth values instead of absolute ones. This logic is based on degrees of membership, which vary between 0 and 1, partially allowing an element to belong to multiple sets [42]. Linguistic variables are defined in fuzzy sets, expressed in natural language, and describe varying degrees of membership. This tool fills a gap compared to other approaches, underlining its importance in providing mathematical results free of subjectivities. In contrast to more conventional methodologies, fuzzy logic stands out for its flexibility in dealing with uncertainty, making it a valuable tool for reasoning and decision-making in complex situations [43].  
Fuzzy sets can be defined with Equation (1):  
\[A=\{(x,\;\mu_{A}\;(x))|x\in U\} \tag{1}\]  
where \(\mu_{A}\): \(x\rightarrow[0,1]\) is the membership function, \(\mu_{A}\;(x)\) is the degree of membership of the variable x, and U is the domain of the application, called in \"fuzzy\" terms the universe in discourse. The closer \(A\) is to the value of 1, the greater the relevance of the object x to the set \(A\).  
* Membership functions: These represent the degree to which an element belongs to a subset defined by a label. They allow us to represent a fuzzy set graphically. The x-axis  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **(+) Positive** & & **(–) Negative** \\ \hline
5 & 4 & 3 & 2 & 1 \\ Strongly Agree & Somewhat Agree & Neither Agree nor Disagree & Somewhat Disagree & Strongly Disagree \\ \hline  & & & & \\ \hline \hline Q1: I think I would like to use this application frequently. & & & \\ \hline Q2: I find this application unnecessarily complex. & & & \\ \hline Q3: I think the application is easy to use. & & & \\ \hline Q4: I think I would need support to use the application. & & & \\ \hline Q5: I find the various functions of the application well integrated. & & & \\ \hline Q6: I have found too much inconsistency in this application. & & & \\ \hline Q7: I think most people would learn to use the application quickly. & & & \\ \hline Q8: I have found the app quite cumbersome to use. & & & \\ \hline Q9: I feel very confident using the app. & & & \\ \hline Q10: I would need to learn many things before operating the app. & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Items System Usability Scale (SUS).  
(abscissa) represents the universe in discourse, while the y-axis (ordinate) represents the degrees of membership in the interval [0, 1]. To define the fuzzy set, the triangular and trapezoidal functions will be used, as shown in Table 4, because they allow for modeling uncertainty and ambiguity and for representing graphically how the degree of belonging of an element to a fuzzy set varies, which is crucial in systems where the binary classification (belonging or not belonging) is too restrictive [44].
* Fuzzy systems: The starting point for building a fuzzy system is to obtain a collection of fuzzy rules based on human knowledge. The next step is to combine these rules into a simple design. Different fuzzy systems employ different principles of this combination; for this purpose, the Takagi-Sugeno-Kang (TSK) fuzzy system will be used for its accuracy in modeling complex and nonlinear relationships, providing clear and accurate numerical outputs [45].
* Defuzzification: An essential mathematical process in fuzzy logic that transforms fuzzy sets into a representative actual number. Although the fuzzy inference system produces conclusions in fuzzy terms, it is required to convert this fuzzy information into a singular real value to obtain a valuable and concrete output. Among the available defuzzification methods, the centroid method will be used, which allows the calculation of the x-coordinate of the center of gravity of the resulting fuzzy set, thus providing a fundamental value that effectively represents the fuzzy conclusion [46].