# Evaluating a Proposed E-Government Stage Model in Terms of Personal Data Protection
## 3 Assessment Methodology
### AHP-SOAR Calculation
In terms of the first level, which is about essential targets, the pairwise comparison utilizes a 3 by 3 matrix to determine the factors by dividing each row element by the total of each target column. The Eigen vectors are then normalized by averaging the factor values over the new rows or adding each new row and dividing by the number of factors, which, in this case, is three. The matrix below shows the pairwise comparison matrix for targets in relation to the goal. For selecting the values of [PERSON]'s table, a questionnaire survey  
Figure 7: The methodology process flow of combining SOAR and AHP. was performed among 20 information security experts from government organizations (8 participants) and IT companies (12 participants) in the Kurdistan region of Iraq. \[W= \begin{bmatrix}\text{T1}&\text{T2}&\text{T3}\\ \text{T1}&&\\ \text{T2}&&\\ \text{T3}&&\\ Sum&&\end{bmatrix} = \begin{bmatrix}1&7&7\\ \frac{1}{2}&1&\frac{1}{2}\\ \frac{7}{2}&2&1\\ \frac{7}{2}&10&\frac{17}{2}\end{bmatrix} \]  
After dividing each matrix element by the sum of its corresponding column, the normalized relative weight will arrive. Each column's total is 1. \[W= \begin{bmatrix}\frac{7}{3}&\frac{7}{10}&\frac{14}{2}\\ \frac{7}{3}&\frac{10}{10}&\frac{34}{2}\\ \frac{7}{3}&\frac{10}{10}&\frac{37}{2}\\ 1&1&1\end{bmatrix} \]  
The principal Eigen vector (Criteria Weight) that is normalized can be derived by averaging the rows. \[W= \begin{bmatrix}\frac{7}{3}&\frac{7}{10}&\frac{14}{2}\\ \frac{7}{3}&\frac{10}{10}&\frac{34}{2}\\ \frac{7}{3}&\frac{10}{10}&\frac{34}{2}\\ 1&1&1\end{bmatrix} = \begin{bmatrix}0.767\\ 0.089\\ 0.142\end{bmatrix} \]  
For calculating the consistency, which is to check whether the calculated value is correct or not, the same pairwise comparison matrix, which is not normalized, must be taken, then one must multiply each value in the column by the criteria weighted value in the criteria weight. \[C= \begin{bmatrix}1*0.767&7*0.089&7*0.142\\ \frac{1}{2}*0.767&1*0.089&\frac{1}{2}*0.142\\ \frac{1}{2}*0.767&20.089&1*0.142\end{bmatrix} \]  
Calculate the weighted sum value by taking the sum of each value in the row, which is  
\[WS= \begin{bmatrix}2.397\\ 0.271\\ 0.432\end{bmatrix} \]  
Calculate the ratio of weighted sum value and criteria weight. \[R= \begin{bmatrix}3.314\\ 3.827\\ 2.100\end{bmatrix} \]  
Calculate Lambda max by taking the average of all values that come from R.  
\[\lambda_{\text{max}}=\frac{3.314+3.827+2.100}{3}=3.080\]  
The consistency index can obtain by Formula (6) in Section 3.2:  
\[CI=\frac{3.080-3}{2}=0.040\]  
The consistency ratio is given by dividing the consistency index with the random index RI. The random index for the targets matrix is 0.58 because the matrix is 3 \(\times\) 3. \[CR=\frac{0.040}{3}=0.069<0.1\]Thus, the matrix is consistent and acceptable because the consistency ration is less than 0.1, therefore, the result of the calculation is true. The same process will also be used for the comparison of SOAR factors to identify the weight of factors within the SOAR group at the second level. In this level, the matrix is 4 by 4. The value of the Weighted factors, Lambda max, and Consistency ratio are calculated below. \[W= \begin{bmatrix}&\text{S}&\text{O}&A&\text{R}\\ \text{S}&&&&\\ \text{O}&&&&\\ \text{A}&&&&\\ \text{R}&&&&\\ Sum&&\end{bmatrix} = \begin{bmatrix}1&3&7&7\\ \frac{1}{3}&1&3&7\\ \frac{1}{3}&\frac{1}{3}&1&3\\ \frac{1}{7}&\frac{1}{3}&1\\ \frac{34}{21}&\frac{94}{21}&\frac{34}{3}&18\end{bmatrix} = \begin{bmatrix}0.574 \\ 0.271\\ 0.104\\ 0.051\end{bmatrix} \]  
\[\lambda_{\text{max}}=\frac{4.316+4.189+4.123+4.031}{4}=4.164\]  
The random index for the Factor matrix is 0.9 because the alternatives (Factors) matrix is 4 \(\times\) 4. \[CR=\frac{0.054}{0.9}=0.060<0.1\]  
The three essential targets (T1, T2, and T2) were subjected to pairwise comparison. The SOAR factors calculated, with respect to each essential target. The matrix below shows the weight of each factor, with respect to T1. \[W=