## 3 Materials and Methods
### The Process of Decision-Making Using the AHP Methodology
\begin{table}
\begin{tabular}{c c c} \hline
**Scale** & **Definition** & **Explanation** \\ \hline
1 & Equal importance & Two activities contribute equally \\
3 & Weak importance & Experience and judgement slightly favor one over another \\
5 & Essential importance & Experience and judgement strongly favor one over another \\
7 & Very strong importance & Experience and judgement very strongly favor one over another; its \\
9 & Absolute importance & \multicolumn{1}{c}{} & \\
2, 4, 6, 8 & Intermediate values & \multicolumn{1}{c}{} & \\ \hline \end{tabular}
\end{table} 
Table 3: [PERSON]’s scale of relative importance [54]. In the case of consistent estimates, the following applies:  
\[a_{ij}=a_{ik}\cdot a_{kj}, \tag{3}\]  
thus fulfilling the condition of the equation,  
\[w=n\cdot w, \tag{4}\]  
where \(w\) denotes the priority vector:  
\[\left[ \begin{array}{cccc}\frac{w_{1}}{w_{1}}&\frac{w_{2}}{w_{2}}&\frac{w_{1}}{ w_{n}}&\frac{w_{1}}{w_{n}}\\ \frac{w_{2}}{w_{1}}&\frac{w_{2}}{w_{2}}&\frac{w_{2}}{w_{n}}\\.&.&.\\ \ldots&\ldots&\ldots&\ldots\\ \frac{w_{n}}{w_{1}}&\frac{w_{n}}{w_{2}}&\frac{w_{n}}{w_{n}}\\ \end{array} \right]\left[ \begin{array}{c}w_{1}\\ w_{2}\\.\\ \ldots\\.\\ \ldots\\.\\ w_{n}\end{array} \right]=n\left[ \begin{array}{c}W_{1}\\ W_{2}\\.\\ \ldots\\.\\ W_{n}\end{array} \right] \tag{5}\]  
Given that any deviation from consistency affects the change in values, the consistency index \(CI\) was determined when using the AHP method [57]:  
\[CI=\frac{\lambda_{\max-n}}{n-1}, \tag{6}\]  
where \(\lambda_{\max}\) denotes the largest value of the comparison matrix, while \(n\) is the number of criteria or alternatives being compared. The smaller the difference between \(\lambda_{\max}\) and \(n\), the greater the consistency will be. The consistency ratio (\(CR\)) is calculated by dividing the consistency index (\(CI\)) by the random consistency index (\(RI\)). If the consistency ratio is 0.10 or less, then the decision-maker's response or assessment is consistent, but if the consistency ratio is higher than 0.10, it is necessary to analyze why the inconsistency occurred, as follows:  
\[CR=\frac{CI}{RI} \tag{7}\]  
where the random consistency index (\(RI\)) represents the already calculated values shown in Table 4 and is used only in the case when \(n\) is greater than 3. Numerous scientists [54; 58; 59; 60; 61; 62; 63; 64; 65; 66] state that the analytic hierarchy process is one of the most desirable methods for decision-making support. Some of the major advantages of the AHP method are as follows:  
* AHP method, which is based on subjective assessments of decision-makers, combines qualitative and quantitative factors in decision-making. * AHP method uses a scale to measure quantitative and qualitative criteria. * AHP method solves a problem by dividing it (branching) into smaller problems,
* AHP method allows for the simulation of the decision-making process (defining the goal, criteria, and alternatives; and comparing them with each other with the aim of obtaining results in relation to the set goal). * AHP method allows the decision-maker to perform a sensitivity analysis of the results, which provides information on how much a change in the importance of a certain \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**N** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(RI\) & 0 & 0 & 0.52 & 0.89 & 1.11 & 1.25 & 1.35 & 1.4 & 1.45 & 1.49 \\ \hline \end{tabular}
\end{table} 
Table 4: Random consistency index values (\(RI\)) [54]. criterion affects the overall results (simulating the relationship between the weights of the criteria and the priorities of the alternatives). * When using the AHP method, tools such as Expert Choice (the most commonly used tool) are used, which easily enables the decision-maker to achieve a given goal. When using the AHP method, certain restrictions occur, which users often encounter, and accordingly, numerous researchers are trying to find ways to eliminate them.