## 2 Literature Review
### The Weight of the Criteria
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Calculation Step** & **A** & **B** & **C** & **D** & **E** & **F** & **G** & **H** & **I** \\ \hline Step one: & \(\omega_{1}^{\prime}\) & \(\omega_{2}^{\prime}\) & \(\omega_{3}^{\prime}\) & \(\omega_{4}^{\prime}\) & \(\omega_{5}^{\prime}\) & \(\omega_{6}^{\prime}\) & \(\omega_{7}^{\prime}\) & \(\omega_{8}^{\prime\prime}\) & \(\omega_{9}^{\prime}\) \\ The elements \(a_{ij}\) of each line in the matrix are multiplied & & & & & & & & & \\ The product of the first line & & & & & & & & & & \\ Result & 0.2222 & 1008 & 245 & 0.0034286 & 0.33333 & 0.00002025 & 60,480 & 11,025 & 0.000001181 \\ \hline Step two: & \(\omega_{1}^{\prime}\) & \(\omega_{2}^{\prime}\) & \(\omega_{3}^{\prime}\) & \(\omega_{4}^{\prime}\) & \(\omega_{5}^{\prime}\) & \(\omega_{6}^{\prime}\) & \(\omega_{7}^{\prime}\) & \(\omega_{8}^{\prime}\) & \(\omega_{9}^{\prime}\) \\ \(n\)-degree root is extracted & & & & & & & & & \\ from \(\omega_{i}^{\prime}\) & & & & & & & & & \\ The root of the products & & & & & & & & & & \\ of the first line & & & & & & & & & & \\ Result & 0.8461 & 2.785 & 1.84274 & 0.5323 & 0.8851 & 0.3009 & 3.3985 & 2.8129 & 0.2195 \\ \hline Step three: The sum of all \(\omega_{1}^{\prime}\) & & & & & & & & & \\ The sum of all constituents & & & & & & & & & \\ \hline Step four: & \(\omega_{1}\) & \(\omega_{2}\) & \(\omega_{3}\) & \(\omega_{4}\) & \(\omega_{5}\) & \(\omega_{6}\) & \(\omega_{7}\) & \(\omega_{8}\) & \(\omega_{9}\) \\ Every element \(\omega_{i}^{\prime}\) is divided & & & & & & & & & \\ from the sum of all elements \(\omega_{i}^{\prime}\) & & & & & & & & & \\ of the first factor is & & & & & & & & & \\ divided from the sum & & & & & & & & & \\ of all elements & & & & & & & & & \\ The Eigenvector is obtained & 0.0621 & 0.2044 & 0.1353 & 0.0391 & 0.0650 & 0.0221 & 0.2495 & 0.2064 & 0.0161 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The sequence (algorithm) of calculating the weight cause (criterion) Eigenvector. Next, the consistency of the matrix filled in by the expert is verified (Table 5). For that purpose, the sum of the products \(\sum\limits_{j=1}^{9}a_{ij}\omega_{j}\) is divided from the value of the calculated Eigenvector \(\omega_{i}\) of a particular factor (criterion) (Table 5). The intermediate calculation results are presented in Table 6.  
The arithmetic mean of the last column in Table 6 equal to the highest Eigenvalue \(\lambda_{max}\) is calculated as:  
\[ \begin{array}{ll}\lambda_{max}=&\frac{1}{n}\sum\limits_{i=1}^{n}\frac{\sum \limits_{i=1}^{n}a_{ij}\omega_{j}}{\omega_{i}}\\ &=\frac{1}{9}(9.4863+9.7290+9.8840+9.6726+9.4246+9.6697+9.7735+7.3406+10.0808)\\ &=9.4478.\end{array} \]  
The consistency index (C.I.) is estimated as:  
\[C.I.=\frac{\lambda_{max}-n}{n-1}=\frac{9.4478-9}{9-1}=0.05598.\]  
The random index (\(R.I.\)) from the table [75] is defined or calculated according to formula (8):  
\[R.I.=\frac{1.98(n-2)}{n}, \tag{8}\]  
when \(n=9\), then \(R.I.=1.45\). The consistency ratio \(C.R.\) is calculated as:  
\[C.R.=\frac{C.I.}{R.I.}=\frac{0.05598}{1.45}=0.0386.\]  
The calculated \(C.R.\) is compared with its critical (maximum allowed) value of 0.1, which is acceptable to make the pairwise comparison matrix \(\mathbf{A}\) consistent. \(C.R.=0.0386\) is less than 0.1, and thus it can reasonably be considered that matrix \(\mathbf{A}\) is consistent and its Eigenvector \(\omega_{i}\) is the relative weight of the criteria.