## 4 Methods
### Combinative Distance-Based Assessment (CODAS) Method  
The alternatives' desirability is assessed by adopting two measures in this approach. The Euclidean distance (ED) between the alternatives and the negative ideal solution (NIS) are the most basic and important metrics. For criteria, the ED implies the usage of al2-norm indifference space. As a supplemental metric, the taxicab distance (TD) is used. The l1-norm indifference space (NIS) is related to it. The alternative that is farthest from the NIS is certainly the best. If the Euclidean distance cannot be used to compare two options, the taxicab distance can be used as a supplemental measure in this technique. Even though CODAS prefers the l2-norm indifference space, the method could also include two additional types of indifference spaces. If, for example, there are \(n\) options and \(m\) criteria from which we have to choose, the following steps are associated with this approach:  
**Step 1.** Construct the decision-making matrix (\(A\)), as illustrated below:  
\[A=\left[a_{ij}\right]_{m\times n}=\left[\begin{array}{cccc}a_{11}&a_{12}& \ldots&a_{1n}\\ a_{21}&a_{22}&\ldots&a_{2n}\\ \ddots&\ddots&\ddots&\ddots\\ a_{m1}&a_{m2}&\ldots&a_{mn}\end{array}\right] \tag{9}\]  
where \(a_{ij}\big{(}a_{ij}\geq 0\big{)}\) signifies the \(i\)th alternative's performance value on the \(j\)th criterion and \((i\in\{1,2,\ldots,m\}\) and \(j\in\{1,2,\ldots,n\})\).  
**Step 2.** Obtain the normalized decision matrix. The following equation demonstrates the linear normalization in relation to the performance values:  
\[N_{ij}=\left\{\begin{array}{ccc}\frac{a_{ij}}{maxa_{ij}}&if&j\in C_{b}\\ \frac{min_{i}a_{ij}}{a_{ij}}&if&j\in C_{nb}\end{array}\right. \tag{10}\]  
where, \(C_{b}\) represents the benefit set and \(C_{nb}\) refers to the cost criteria set.  
**Step 3.** Calculate the normalised weighted decision matrix. The following formula is utilized to determine the weighted normalized performance values:  
\[WN_{ij}=w_{j}N_{ij} \tag{11}\]  
where, \(w_{j}\) (\(0<w_{j}<1\)) indicates the weight related to the \(j\)th criterion, and \(\sum\limits_{j=1}^{n}w_{j}=1\)  
**Step 4.** Obtain the NIS point as follows:  
\[NS=\left[NS_{j}\right]_{1\times n} \tag{12}\]  
\[NS_{j}=\underset{i}{min}WN_{ij} \tag{13}\]  
**Step 5.** Compute the ED and TD of the alternatives that are derived using negativeideal solutions, as shown below:  
\[ED_{i}=\sqrt{\sum\limits_{j=1}^{n}(WN_{ij}-NS_{j})^{2}} \tag{14}\]  
\[TD_{i}=\sum\limits_{j=1}^{n}\left|WN_{ij}-NS_{j}\right| \tag{15}\]  
**Step 6.** Create the relative assessment matrix, as shown below:  
\[AM=\left[P_{ik}\right]_{n\times n} \tag{16}\]  
\[P_{ik}=\left(ED_{i}-ED_{k}\right)+\left(\psi(ED_{i}-ED_{k})\times(TD_{i}-TD_{k })\right) \tag{17}\]  
where, \(k\in\{1,2,\ldots,m\}\) and \(\psi\) defines a threshold function for recognizing the equality of two alternatives' Euclidean distances. This threshold function is stated as follows:  
\[\psi(a)=\left\{\begin{array}{ccc}1&if&|a|\geq\tau\\ 0&if&|a|<\tau\end{array}\right. \tag{18}\]  
The value \(\tau\) denotes the threshold parameter specified by the decision-maker in this function. This option should be set between 0.01 and 0.05. When the difference in ED between two alternatives is smaller than \(\tau\), the taxicab distance is employed to compare them. For performing the calculations, \(\tau\) = 0.02 has been taken in this study.  
**Step 7.** Calculate each alternative's assessment score, using the equation below:  
\[AS_{i}=\sum\limits_{k=1}^{m}P_{ik} \tag{19}\]  
**Step 8.** Rank the alternatives, depending on the order of decreasing assessment score \(AS_{i}\) values. Among the alternatives, the option with the greatest \(AS_{i}\) is the best choice.