# Health Project Prioritization in Meta, Colombia, Using Anp-Dematel
## 3 Materials and Methods
### Calculation of the Limit Matrix  
The authors derived the limit matrix by exponentiating the weighted matrix to progressively higher powers until column convergence was achieved. The resulting identical column values (\"raw values\") represent the relative influence of each network element. The final priorities were determined by normalizing these raw values for both criteria and  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & & \multicolumn{2}{c}{**C.1**} & \multicolumn{2}{c}{**C.2**} & \multicolumn{2}{c}{**C.3**} & \multicolumn{2}{c}{**C.4**} & \multicolumn{2}{c}{**C.5**} \\ \cline{3-11}  & & **C.1.1** & **C.1.2** & **C.2.1** & **C.2.2** & **C.3.1** & **C.3.2** & **C.4.1** & **C.4.2** & **C.5.1** & **C.5.2** \\ \hline \multirow{2}{*}{C.1} & C.1.1 & 0.000 & 1.000 & 0.000 & 0.500 & 0.000 & 0.000 & 1.000 & 0.500 & 0.000 & 0.000 \\  & C.1.2 & 1.000 & 0.000 & 0.000 & 0.500 & 0.000 & 0.000 & 0.000 & 0.500 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{C.2} & C.2.1 & 0.000 & 0.000 & 0.000 & 1.000 & 0.000 & 0.000 & 0.667 & 0.333 & 0.000 & 1.000 \\  & C.2.2 & 1.000 & 1.000 & 1.000 & 0.000 & 0.000 & 0.000 & 0.333 & 0.667 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{C.3} & C.3.1 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 1.000 & 0.500 & 0.200 & 1.000 & 1.000 \\  & C.3.2 & 0.000 & 0.000 & 0.000 & 0.000 & 1.000 & 0.000 & 0.500 & 0.800 & 1.000 & 1.000 \\ \hline \multirow{2}{*}{C.4} & C.4.1 & 0.500 & 0.500 & 0.833 & 0.833 & 0.833 & 0.833 & 0.000 & 1.000 & 1.000 & 1.000 \\  & C.4.2 & 0.500 & 0.500 & 0.167 & 0.167 & 0.167 & 0.167 & 1.000 & 0.000 & 0.000 & 0.000 \\ \hline \end{tabular} The full names and definitions of the criterion codes used in the table are provided in Table 1.  
\end{table}
Table 7: Normalized influence matrix of elements using DEMATEL, according to one expert.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & **C.1.1** & **C.1.2** & **C.2.1** & **C.2.2** & **C.3.1** & **C.3.2** & **C.4.1** & **C.4.2** \\ \hline \multirow{2}{*}{C.1} & C.1.1 & 0.000 & 0.000 & 0.000 & 0.083 & 0.000 & 0.000 & 0.179 & 0.089 \\  & C.1.2 & 0.000 & 0.000 & 0.000 & 0.083 & 0.000 & 0.000 & 0.000 & 0.089 \\ \hline \multirow{2}{*}{C.2} & C.2.1 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.119 & 0.060 \\  & C.2.2 & 0.190 & 0.190 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.060 & 0.119 \\ \hline \multirow{2}{*}{C.3} & C.3.1 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.071 & 0.029 \\  & C.3.2 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.071 & 0.114 \\ \hline \multirow{2}{*}{C.4} & C.4.1 & 0.119 & 0.119 & 0.189 & 0.174 & 0.185 & 0.185 & 0.000 & 0.000 \\  & C.4.2 & 0.119 & 0.119 & 0.038 & 0.035 & 0.037 & 0.037 & 0.000 & 0.000 \\ \hline \end{tabular} The full names and definitions of the criterion codes used in the table are provided in Table 1.  
\end{table}
Table 8: Weighted matrix.  
alternatives. Appendix Table A3 presents the complete matrices and priorities assigned by Expert E1.  
The full methodological workflow--including stakeholder identification, criteria definition, and the ANP-DEMATEL prioritization process--is illustrated in Figure 3.