## 5 Fuzzy Model
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Label** & **Description of the Membership Function** \\ \hline \multirow{7}{*}{Ease of Use} & \multirow{3}{*}{Low} & It would cover SUS scores from \(0\) to around \(60\), with full membership at \(0\) and decreasing linearly until reaching \(60\), where membership would be \(0\). \\  & & \(\mu_{Fhaija}(x):\max\Big{(}0,min\Big{(}1,\frac{60-x}{60}\Big{)}\Big{)}\,para\, 0\leq x\leq 60\) \\  & & It would be centered around the average score of \(50\), starting to increase from \(40\), \\  & & peaking at \(60\), and then decreasing to \(80\). \\  & & \(\mu_{Fmedia}(x):\max\Big{(}0,min\Big{(}\frac{x-40}{20},1,\frac{80-x}{20}\Big{)} \Big{)}\,para\,40\leq x\leq 80\) \\  & & \(\mu_{Faltha}(x):\max\Big{(}0,min\Big{(}1,\frac{x-60}{40}\Big{)}\Big{)}\,para \,60\leq x\leq 100\) \\ \hline \multirow{7}{*}{Satisfaction} & \multirow{3}{*}{Dissatisfied} & Full membership would be at \(-3\) (very dissatisfied) and decrease to \(0\). \\  & & \(\mu_{Sinsatisfecho}(x):\max\Big{(}0,min\Big{(}1,\frac{x-x+3}{3}\Big{)}\Big{)}\,para -3\leq x\leq 0\) \\ \cline{2-3}  & & This function would gradually increase from \(-1\) until reaching full membership at \(0\) and decreasing again towards \(1\). \\  & & \(\mu_{Sneutral}(x):\max\Big{(}0,min\Big{(}\frac{x+1}{1},1,\frac{1-x}{1}\Big{)} \Big{)}\,para-1\leq x\leq 1\) \\ \cline{2-3}  & & It would start to increase at \(0\) and reach full membership at \(2\) and would be maintained until \(3\). \\ \hline \multirow{7}{*}{Efficiency} & \multirow{3}{*}{Low} & A long time to complete a task (say more than \(200\) s) would have a high membership at low efficiency. \\  & & \(\mu_{Ehaija}(x):\max\Big{(}0,min\Big{(}1,\frac{500-x}{300}\Big{)}\Big{)}\,para \,200\leq x\) \\  & & A moderate task time (between \(100\) and \(500\) s) would be associated with \\  & & medium efficiency. \\  & & \(\mu_{Emedia}(x):\max\Big{(}0,min\Big{(}\frac{x-100}{400},1,\frac{500-x}{400} \Big{)}\Big{)}\,para\,100\leq x\leq 500\) \\ \cline{2-3}  & & High & A short task time (less than \(300\) s) would indicate high efficiency. \\  & & \(\mu_{Ealtha}(x):\max\Big{(}0,min\Big{(}1,\frac{300-x}{300}\Big{)}\Big{)}\,para \,x\leq 300\) \\ \hline \multirow{7}{*}{Probability of Recommendation} & \multirow{3}{*}{Medium} & If both ease of use and satisfaction are moderate, the likelihood of recommendation would be medium. \\  & & \(\mu_{Emedia}(x):\max\Big{(}0,min\Big{(}1,\frac{300-x}{300}\Big{)}\Big{)}\,para \,x\leq 300\) \\ \cline{1-1} \cline{2-3}  & & \(\mu_{Ealtha}(x):\max\Big{(}0,min\Big{(}1,\frac{300-x}{300}\Big{)}\Big{)}\,para \,x\leq 300\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Description of variable labels. 3. Fuzzy Inference Rules Based on the membership functions, we define rules to infer the probability of recommendation and the overall quality of user experience: * If ease of use is high and satisfaction is high, then the likelihood of recommendation is high. \[Rule\ 1=\text{if}\ \min\Big{(}\mu_{F_{high}}(x),\ \mu_{S_{high}}(x)\Big{)}\ \text{then}\ \mu_{D_{high}}(y)\] where \(\mu_{F_{high}}(x)\) and \(\mu_{S_{high}}(x)\) are the membership functions for ease of use and satisfaction, respectively, evaluated at the \"high\" level. * If ease of use is low or satisfaction is low, then the overall quality of experience is low. \[Rule\ 2=\text{if}\ \max\big{(}\mu_{F_{low}}(x),\ \mu_{S_{low}}(x)\big{)}\ \text{then}\ \mu_{D_{low}}(y)\] where \(\mu_{F_{low}}(x)\) and \(\mu_{S_{low}}(x)\) are the membership functions for ease of use and satisfaction, respectively, evaluated at the \"low\" level. * If efficiency is low, then the overall quality of experience is low, regardless of the ease of use and satisfaction. \[Rule\ 3=if\ \mu_{E_{low}}(x)\ \text{then}\ \mu_{Q_{low}}(y)\] where \(\mu_{E_{low}}(x)\) is the membership function for efficiency evaluated at the \"low\" level. * If the ease of use is high, satisfaction is high, and efficiency is high, then the quality of the user experience is good.