## 2 Methodology
This centroid defuzzification technique successfully converts fuzzy numbers into single numbers, enabling their consideration in the analysis process. The PROMETHEE technique with a Gaussian preference function was utilized. This choice was made because the Gaussian preference function is robust to outliers and extreme values, thereby enabling a more balanced and rational comparison between alternatives. It offers flexibility in deriving preferences for decision makers, considering mean and standard deviation to match the decision context. Gaussian preferences facilitate a smooth transition between preference levels, resulting in a gradual change in preference rather than abrupt shifts. Furthermore, prioritizing alternatives by considering a parameters' standard deviation ensures that preference values are relatively sensitive, thus establishing the resulting ranking order. As seen in Table 1, 15 parameters and their importance weights were utilized for each class assessment and 5 intorpe alternatives were compared and placed in a decision matrix. The intorpes dataset of the chronic HFrEF patients is shown in Table 2.  
As seen in Tables 1 and 2, each parameter is graded from VL to VH according to its importance levels and with Min or Max according to its aim based on the expert's priorities. The values are also subject to further grading as necessary to be viable for the F-PROMETHEE technique. It is important to note that parameter values are not subject to change when evaluating for different classes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Criteria/Alternatives** & **Aim/Imp. ** & **Weights** & \begin{tabular}{c} **Adrenaline** \\ **(\$1 \textgreater{} \textgreater{} \text@{\text@{\text@{\text@{}}}}2 \textgreater{} \text@{\text@{\text@{\text@{}}}}\alpha)** \\ \end{tabular}  & \begin{tabular}{c} **Noradrenalineine** \\ **(\$10 \textgreater{} \text@{\text@{\text@{}}}2 \textgreater{} \text@{\text@{\text@text@{}}}\alpha)** \\ \end{tabular}  & \begin{tabular}{c} **Dopamine** \\ **(\$10 \text@{\text@{\text@{}}}2, \\ \text@{\text@{\text@{}}}\alpha\text@{\text@{\text@{}}}\text@{\text@{\text@{ }}}\text@{\text@{\text@{}}}}\)** \\ \end{tabular}  & \begin{tabular}{c} **Dobutamine** \\ **(\$10 \text@{\text@{\text@{}}}2 \textgreater{} \text@{\text@{\text@{}}}\text@{\text@{\text@{}}}\text@{\text@{\text@{}}} \text@{\text@{}}\alpha)** \\ \end{tabular}  & \ \begin{tabular}{c} **Milrinone** \\ **(\$10 \text@{\text@{\text@{}}}2 \textgreater{} \text@{\text@{\text@{}}}\text@{\text@{\text@{}}}\text@{\text@{}} \text@{\text@{}}\text@{\text@{}}\alpha)** \\ \end{tabular}  \\ \hline \multirow{2}{*}{Cost} & \multirow{2}{*}{Min} & \multirow{2}{*}{VL} & 271 USD/ & 120 USD/ & 141 USD/ & 136 USD/ & 55.70 USD/ \\  & & & 30 mL & 40 mL & 3000 mL & 3000 mL & 200 mL \\  & & & (30 mg) & (40 mg) & (4800 mg) & (6000 mg) & (200 mg) \\ \hline \multirow{2}{*}{ \begin{tabular}{c} Steady-State Blood \\ Concentration \\ Reached In \\ \end{tabular}  } & \multirow{2}{*}{Min} & \multirow{2}{*}{VH} & \multirow{2}{*}{10–15 min} & \multirow{2}{*}{5 min} & \multirow{2}{*}{5 min} & \multirow{2}{*}{10 min} & \multirow{2}{*}{20 min} \\  & & & & & & & \\ \hline Half-Life & \multirow{2}{*}{Min} & \multirow{2}{*}{M} & \multirow{2}{*}{3 min} & \multirow{2}{*}{2.4 min} & \multirow{2}{*}{2 min} & \multirow{2}{*}{2 min} & \multirow{2}{*}{2 min} & \multirow{2}{*}{2.5 h} \\ \hline Long-Term Use & \multirow{2}{*}{Max} & \multirow{2}{*}{M} & \multirow{2}{*}{VL}  
Thus, it is now possible to utilize the F-PROMETHEE to rank the intorrope alternatives according to acute-phase or chronic-phase HFrEF. They each have different assigned importance weights and parameter aims and are expected to yield different ranking orders.