## 2 Hybrid MCDM Model  
In this paper, a new hybrid MCDM model is proposed, which is a combination of Fuzzy SWARA [32] and ADAM [43] methods. Within the methodology, Fuzzy SWARA is applied to determine the relative weights of the criteria, and the ADAM method is used to rank alternative solutions. The Fuzzy SWARA method is resolved using the mathematical formulation outlined in the paper and implemented through an Excel solver. The ADAM method was tackled using a dedicated software tool that is conveniently accessible online [46]. Below is a step-by-step description of the methodology. Step 1: Define the problem structure  
In the first step, the structure of the problem is defined through the analysis of a set of alternatives and criteria. These criteria are used to evaluate alternatives. Step 2: Defining evaluation scales  
In this step, the scale of linguistic evaluations that decision makers use to evaluate criteria and alternatives is defined. The scale of linguistic evaluations with the associated fuzzy and crisp numbers is given in Table 1.  
In this step and in accordance with the Fuzzy SWARA method, decision makers rank the criteria. The criteria are ranked in descending order of importance. Step 4: Evaluation of the importance of criteria  
After ranking the criteria, decision makers evaluate the relative importance of criterion \(j\) compared to the other criteria \((j-1)\), beginning with the second criterion. This relation is called the comparative significance of the average value and is denoted as \(\widetilde{\alpha}_{j}\), where \(\widetilde{\alpha}_{j}=\left(l_{j},\ m_{j},u_{j}\right)\), \(j=1,\ldots,m\), denotes triangular fuzzy values that correspond to the given linguistic terms in Table 1, and \(l,\ m\), and \(u\) denote the lower, middle, and upper values of the triangular fuzzy number, respectively. Step 5: Coefficient calculation \(\widetilde{\beta}_{j}\)  
After evaluating the criteria, coefficient \(\widetilde{\beta}_{j}\) is calculated. The mathematical formula for the calculation of coefficient \(\widetilde{\beta}_{j}\) is given below. \[\beta_{j}=\left\{ \begin{aligned} &(1,\ 1,\ 1),\ j=1\\ &\left(\frac{l_{j}}{\frac{\max}{j}}\,\frac{m_{j}}{\max}\,\frac{u_ {j}}{\max}\,\frac{u_{j}}{\max}\,\frac{u_{j}}{\max}\,\frac{u_{j}}{\max}\,u\right) +(1,\ 1,\ 1),\ j>1,\ldots,m^{\prime}\end{aligned} \right. \tag{1}\]  
Step 6: Calculation of the preliminary weight of the criteria \(\widetilde{\delta}_{j}\)  
Based on the results from Step 5, the preliminary value of the criterion weights, \(\widetilde{\delta}_{j}\), is calculated as follows:  
\[\widetilde{\delta}_{j}=\left\{ \begin{aligned} &(1,\ 1,\ 1),\ j=1\\ &\frac{\widetilde{\delta}_{j-1}}{\widetilde{\beta}_{j}}+(1,\ 1,\ 1),\ j>1,\ldots,m^{\prime}\end{aligned} \right. \tag{2}\]  
Step 7: Calculation of the relative weight of the criteria \(\widetilde{w}_{j}\)  
After the calculation of the preliminary weight of the criteria, the relative weight of the criteria, \(\widetilde{w}_{j}\), is calculated as follows:  
\[\widetilde{w}_{j}=\frac{\widetilde{\delta}_{j}}{\sum\widetilde{\delta}_{j}}, \tag{3}\]  
Step 8: Defining the matrix \(\widetilde{F}\)  
In the second part of the methodology, the ADAM method is used to determine the ranking of alternatives. After obtaining the relative weights of the criteria using the Fuzzy \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Linguistic Evaluation** & **Abbreviation** & **Fuzzy Scale** & **Crisp Scale** \\ \hline “Non” & “N” & (1, 1, 2) & 1 \\ “Very Low” & “Vl” & (1, 2, 3) & 2 \\ “Low” & “L” & (2, 3, 4) & 3 \\ “Fairly Low” & “FL” & (3, 4, 5) & 4 \\ “Medium” & “M” & (4, 5, 6) & 5 \\ “Fairly High” & “FH” & (5, 6, 7) & 6 \\ “High” & “H” & (6, 7, 8) & 7 \\ “Very High” & “VH” & (7, 8, 9) & 8 \\ “Extremely High” & “EH” & (8, 9, 10) & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation scale for the comparison of criteria/alternatives. SWARA method, it is necessary to define the input parameters for the ADAM method.