## 3 Proposed Methodology
### Hybrid Multi-Criteria Decision Analysis (MCDA)
#### 3.4.2 MCDA Ranking  
* TOPSIS:  
The TOPSIS method evaluates the relative closeness of each alternative to the ideal solution. The decision matrix is normalized and weighted, and then the Euclidean distance of each alternative to the ideal and anti-ideal solutions is calculated:  
\[S_{i}^{+}=\sqrt{\sum_{j=1}^{n}\bigl{(}v\text{ij}-v_{i}^{+}\bigr{)}^{2}} \tag{4}\]  
\[S_{i}^{-}=\sqrt{\sum_{j=1}^{n}\bigl{(}v\text{ij}-v_{i}^{-}\bigr{)}^{2}} \tag{5}\]
* SAW:  
The fundamental principle behind the SAW method involves determining the weighted performance ratings for each alternative across all attributes [21]. The alternative with the highest score is considered the optimal choice. \[rij=\frac{xij}{\text{max}xij}\text{ i = 1,2,3,4, \text{mj = 1,2,3,\ldots,16}} \tag{6}\]  
\[rij=\frac{xij}{\text{min}xij}\text{ i = 1,2,3,4, \text{mj = 1,2,3,\ldots,16}} \tag{7}\]  
The favorite value for each alternative (Vi) is given as:  
\[\text{Vi}=\sum_{j=1}^{n}wjrij\text{ i = 1,2,3,4} \tag{8}\]
* VIKOR:In VIKOR each alternative is gauged according to all deemed criteria and the middle ground ranking is applied by assessing how close the measurement is to the ideal alternative [45]. \[f_{j}^{*}=maxx_{ij}.f_{j}^{-}=minx_{ij}\;j=1,2\ldots n \tag{9}\]  
\[f_{j}^{-}=minx_{ij}.f_{j}^{-}=maxx_{ij}\;j=1,2\ldots n \tag{10}\]  
\[S_{i}=\sum_{j=1}^{6}w_{j}\left(f_{j}^{*}-x_{ij}\right)/\left(f_{j}^{*}-f_{j}^{- }\right) \tag{11}\]  
\[R_{i}=max\left[w_{j}\left(f_{j}^{*}-x_{ij}\right)/\left(f_{j}^{*}-f_{j}^{-} \right)\right] \tag{12}\]  
* PROMETHEE II  
There are PROMETHEE I and PROMETHEE II. The first delivers partial ranking, whereas the second version is applied for full ranking. PROMETHEE II is used in this research. There are five steps to prepare PROMETHEE to be deployed as follows [42]:  
1. Normalize the decision matrix
2. Assess the evaluative variances of option \(i\) compared with the remaining alternatives. 3. A preference function \(P_{j}\) is a function of the contrast between evaluations of two criteria (\(a\) and \(b\)), indicated as \(P_{j}(a,b)\). There are six types of preference functions; Type 1 has been used in this research, which is \(p=\left\{ \begin{array}{ll}0,&if\;d<0\\ 1,&if\;d\geq 0\end{array} \right.\)
4. The multi-criteria preference index \(\Pi\) is subsequently characterized as the weighted mean of the preference functions. 5. Establish the leaving and entering outranking flows, in which \(m\) is the of alternatives while each alternative has to deal with \((m-1)\) number of other options as below. Leaving (or positive) flow for the \(I\) alternative that presents how dominant each alternative is compared with the rest:  
\[\varphi^{+}(a)=\frac{1}{m-1}{\sum_{b=1}^{m}\pi(a,b)(a\
eq b)} \tag{13}\]  
Entering (or negative) flow for the \(I\) alternative, which represents how dominant other alternatives are when facing each one:  
\[\varphi^{-}(a)=\frac{1}{m-1}{\sum_{b=1}^{m}\pi(b,a)(a\
eq b)} \tag{14}\]  
1. Compute the gross outranking flow for each option, as shown below \(\varphi(a)\) belongs to the alternative \(a\): \[\varphi(a)=\varphi^{+}(a)-\varphi^{-}(a)\] (15)
2. Seeking the best alternative by looking at the \(\varphi(a)\) value as the highest one will best interpret the variance of leaving flow with entering flow as the most significant [42]. 3. COPRAS: The COPRAS method is defined in the following steps:  
1. A decision matrix (D\({}_{\text{m}\times\text{n}}\)) is formed and normalized. 2. The sum total of the weighted normalized values is specified using S\({}_{+i}\) for profit criteria and S\({}_{-i}\) for cost criteria: \[S_{+i}=\sum_{j=1}^{k}v_{ij}\] (16)\[S_{-i}=\sum_{j=k+1}^{6}v_{ij} \tag{17}\]  
where \(k\) is the number of profit/benefit criteria, and the rest of the criteria from \(k+1\) to \(n\) are the number of cost criteria. The \(S_{+i}\) and \(S_{-i}\) values show the degree of accomplishment of the objective for alternatives. A higher value for \(S_{+i}\) and a lower value for \(S_{-i}\) points to better alternatives. 1. Determine the comparative importance of alternatives. 2.