## 2 Materials and Methods
### ELECTRE Method  
The ELECTRE method, developed by [PERSON] in 1968, is a technique utilized for multi-criteria decision-making problems. It was introduced to address the shortcomings observed in other decision-making approaches [16]. While initially employed for selecting the best alternative, this method has been subsequently adapted for use in ranking and classification problems. There are six variations of the ELECTRE method documented in the literature. The ELECTRE I method, initially proposed, has been applied in selection problems. Later, the ELECTRE II method was devised for ranking periodicals in media planning. The ELECTRE III method was developed to address the adverse impacts of incomplete information and to manage uncertainty by incorporating threshold values. The ELECTRE IV method was subsequently developed for ranking without factoring in the importance coefficients, specifically for a problem concerning the metro network. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**N Value** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** \\ \hline
**RI Value** & 0 & 0 & 0.58 & 0.89 & 1.12 & 1.24 & 1.32 & 1.41 & 1.45 & 1.49 & 1.51 & 1.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Random index values. The method incorporates outranking relations. In the ELECTRE IS method, artificial criteria are considered in cases where the data are imprecise, facilitating the selection of alternatives. The ELECTRE TRI method was developed to address the loan request challenges encountered by a bank. It was developed to tackle the challenge of assigning alternatives to predefined categories. Table 3 summarizes information about these methods [17]. At the core of all ELECTRE methods lies the preference of alternatives based on outranking. The ELECTRE method generally consists of the steps shown in Figure 3[18]. Create decision matrix: First, the decision matrix for the problem is constructed. In this matrix, the rows represent alternatives, while the columns represent criteria. This matrix is referred to as matrix A. The initial matrix A contains the scores of each alternative for each criterion as determined by the decision maker. Matrix A is shown in Equation (8). \[A_{ij}= \begin{bmatrix}a_{11}&a_{12}&\dots&a_{1n}\\ a_{21}&a_{22}&\dots&a_{2n}\\.&&.\\.&&&.\\.&&&.\\ a_{m1}&a_{m2}&\dots&a_{mn}\\ \end{bmatrix}  \tag{8}\]  
Figure 3: Steps of the ELECTRE method. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**ELECTRE Method** & **Proposed by** & **Emerged in** & **Purpose** \\ \hline ELECTRE I & [PERSON] & 1968 & Selection \\ ELECTRE II & [PERSON] and [PERSON] & 1971 & Ranking \\ ELECTRE III & [PERSON] & 1978 & Ranking \\ ELECTRE IV & [PERSON] and [PERSON] & 1982 & Ranking \\ ELECTRE IS & [PERSON] and [PERSON] & 1985 & Selection \\ ELECTRE TRI & [PERSON], [PERSON] and [PERSON] & 1991–1992 & Assignment \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Development of ELECTRE methods. In matrix A, as represented in Equation (8), m is the number of alternatives, n is the number of criteria and \(a_{ij}\) is the importance score of alternative m for criterion n.  
Normalize decision matrix: Each element of the decision matrix is normalized within the range [0,1]. It is important to note that separate equations are employed for criteria to be maximized and those to be minimized. Equation (9) is used for the criteria to be maximized, while Equation (10) is used for the criteria to be minimized. \[x_{ij}=\frac{a_{ij}}{\sqrt{\sum_{k=1}^{m}a_{kj}^{2}}} \tag{9}\]  
\[x_{ij}=\frac{\frac{1}{a_{ij}}}{\sqrt{\sum_{k=1}^{m}\left(\frac{1}{a_{ij}} \right)^{2}}} \tag{10}\]  
The normalized decision matrix is shown in Equation (11). \[X_{ij}= \begin{bmatrix}x_{11}&x_{12}&\dots&x_{1n}\\ x_{21}&x_{22}&\dots&x_{2n}\\ \cdot&&\cdot\\ \cdot&&&\cdot\\ \cdot&&&\cdot\\ x_{m1}&x_{m2}&\dots&x_{mn}\end{bmatrix}