## 2 Materials and Methods
### ELECTRE Method
 \tag{11}\]  
Construct weighted normalized decision matrix: In the normalized decision matrix, the values in each column are multiplied by the importance values assigned to that criterion. Here, the weights are shown as \(w_{i}\). The normalized decision matrix, \(Y_{ij}\), is calculated as shown in Equation (12) and presented as shown in Equation (13). \[Y_{ij}=w_{i}*X_{ij} \tag{12}\]  
\[Y_{ij}= \begin{bmatrix}w_{1}x_{11}&w_{2}x_{12}\dots&w_{n}x_{1n}\\ w_{1}x_{21}&w_{2}x_{22}\dots&w_{n}x_{2n}\\ \cdot\\ w_{1}x_{m1}&w_{2}x_{m2}\dots&w_{n}x_{mn}.\end{bmatrix}  \tag{13}\]  
Determine concordance and discordance sets: Once the weighted normalized decision matrix is established, the alternatives are compared with each other pairwise. These comparisons lead to the formation of concordance and discordance sets. The concordance set is denoted as C (a,b), while the discordance set is denoted as D (a,b), with the number of concordance sets being equal to the number of discordance sets. The number of matching sets is of size (m \(\times\) m \(-\) m) due to the condition that the values of a and b are not equal to each other. The set C (a,b) is calculated as shown in Equation (14) and the set D (a,b) is calculated as shown in Equation (15). \[C(a,b)=\left\{j,\ \ Y_{aj}\geq Y_{bj}\right\} \tag{14}\]  
\[D(a,b)=\left\{j,\ \ Y_{aj}<Y_{bj}\right\} \tag{15}\]  
Determine concordance and discordance indexes: Concordance and discordance matrices are formulated by considering the concordance and discordance sets obtained in the preceding step along with their respective weights. The concordance matrix C is derived by summing the weights of the criteria within the concordance set. The calculation of indexes for the concordance matrix is shown in Equation (16). \[c_{ab}=\sum_{j\in C\ (a,b)}w_{j} \tag{16}\]  
The discordance matrix \(D\) is calculated by the formula provided in Equation (17). \[d_{ab}=\frac{max\left|\ \ Y_{aj}-Y_{bj}\ (j\ \in D(a,b))\right|}{max\left|\ \ Y_{aj}-Y_{bj}\right|} \tag{17}\]  
Conduct outranking comparison: Once the concordance and discordance matrices are determined, concordance and discordance outranking matrices are established. When constructing the concordance outranking matrix, the threshold value, which is the average of the concordance indexes, is initially determined. The calculation of this value is shown in Equation (18). \[C_{\text{esik}}=\frac{1}{\text{m}(\text{m}-1)}\sum_{a=1}^{\text{m}}\sum_{b=1}^{ \text{m}}c_{\text{ab}} \tag{18}\]  
Subsequently, by comparing the values in the concordance matrix with these threshold values, the elements of the \(\text{E}(\text{a},\text{b})\) concordance outranking matrix are determined. Equation (19) shows this comparison. \[\text{e}_{\text{ab}}= \begin{cases}\text{e}_{\text{ab}}=1&\text{c}_{\text{ab} }\geq\ \text{C}_{\text{esik}}\\ \text{e}_{\text{ab}}=0&\text{c}_{\text{ab}}<\text{C}_{\text{esik}}\end{cases}  \tag{19}\]  
When constructing the discordance outranking matrix, the threshold value, which is the average of the discordance indexes, is initially determined. The calculation of this value is shown in Equation (20). \[\text{D}_{\text{esik}}=\frac{1}{\text{m}(\text{m}-1)}\sum_{a=1}^{\text{m}}\sum _{b=1}^{\text{m}}d_{\text{ab}} \tag{20}\]  
Subsequently, by comparing the values in the concordance matrix with these threshold values, the elements of the \(\text{F}(\text{a},\text{b})\) concordance outranking matrix are determined. Equation (21) shows this comparison. \[\text{f}_{\text{ab}}= \begin{cases}\text{f}_{\text{ab}}=1&\text{d}_{\text{ab} }<\text{D}_{\text{esik}}\\ \text{f}_{\text{ab}}=0&\text{d}_{\text{ab}}\geq\ \text{D}_{\text{esik}}\end{cases}  \tag{21}\]  
Rank alternatives by net indexes: The outranking values are computed by multiplying the values in matrix \(\text{E}\), the concordance outranking matrix, by the values in matrix \(\text{F}\), the discordance outranking matrix. These outranking values consist of values of 1 and 0, similar to the concordance and discordance matrices.