# Binary Decision Support Using AHP: A Model for Alternative Analysis
## 4 Case Study
### Definition of Priority Vectors Opposed to ICT  
We conducted an inverse analysis to validate the decision-making framework by defining priority vectors for the alternative classification (i.e., non-ICT). This step ensured that the Binary AHP methodology remained consistent when we applied it to opposing alternatives--ICT and non-ICT classifications--without requiring an entirely new evaluation process. The inverse priority vector approach enabled the decision-makers to analyze how the classification changed when considering the same evaluation criteria from the opposite perspective. This methodology ensured that the decision framework remained balanced, unbiased, and adaptable to different classification contexts. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Subcriterion** & **VPC** & **VPS** & **VPG** \\ \hline \hline \multirow{5}{*}{The solution sought to meet the following need (intended for exclusive use by the MJSP)} & 1.1. Priority area in the strategic plan and aligned with the general IT strategy & 0.29 & 0.04 \\ \cline{2-4}  & 1.2. Priority area in the strategic plan & 0.13 & 0.02 \\ \cline{2-4}  & 1.3. Final area & 0.06 & 0.01 \\ \cline{2-4}  & 1.4. Average priority area in the strategic plan and aligned with the general IT strategy & 0.14 & 0.15 & 0.02 \\ \cline{2-4}  & 1.5. Average priority area in the strategic plan & 0.08 & 0.01 \\ \cline{2-4}  & 1.6. Middle area & 0.03 & 0.01 \\ \cline{2-4}  & 1.7. The following will be donated to organizations outside the MJSP & 0.26 & 0.04 \\ \hline \hline \multirow{5}{*}{Accurate IT solution after deployment} & 2.1. Because it generates data, including personal data, which needs to be collected, stored, and/or processed, it requires attention to cybersecurity & 0.66 & 0.38 \\ \cline{2-4}  & 2.2. To maintain or support software and hardware & 0.57 & 0.14 & 0.08 \\ \cline{2-4}  & 2.3. To maintain or support software or hardware & 0.14 & 0.08 \\ \cline{2-4}  & 2.4. No IT need & 0.07 & 0.04 \\ \hline \multirow{5}{*}{Does the solution involve multimedia, telecommunications, engineering services?} & 3.1. The solution involves multimedia & 0.14 & 0.04 \\ \cline{2-4}  & 3.2. The solution involves telecommunications, or 3.3. The solution involves engineering services? & 0.33 & 0.09 \\ \cline{2-4}  & 3.3. The solution involves engineering services? & 0.05 & 0.01 \\ \cline{2-4}  & 3.4. The solution does not involve these services & 0.49 & 0.14 \\ \hline Total & - & - & 3.00 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Computation of the global priority vector (VPG) based on the AHP weights. The global priority vector values obtained by multiplying the criterion and subcriterion priority vectors. In the reversal process, we maintained the original decision hierarchy and inverted the weight distribution so that the criteria that favored the ICT classification now supported the non-ICT classification, while the criteria that previously weakened the ICT classification now strengthened the non-ICT alternative. This approach eliminated redundancy because it prevented the need for a separate decision model and allowed for a comprehensive evaluation of both possibilities. Table 13 displays the inverted pairwise comparison matrix between the main criteria, which was recalculated for the non-ICT classification alternative. This table also presents the updated priority vector and consistency ratio for the criteria in the non-ICT scenario. In contrast, Table 14 provides the recalculated pairwise comparison matrix for the subcriteria under Criterion 1, specifically for the non-ICT classification. This table details the priority vectors for each subcriterion and the corresponding consistency ratio, reflecting the evaluation of alternatives within this specific criterion. This process ensured the robustness of the decision-making model, as the priority weights remained consistent when classifying a solution as either ICT or non-ICT.