# Exploring Analytical Hierarchy Process for Multicriteria Assessment of Reinforced Concrete Slabs
## 3 Results
In this category, four principal components were used for the dataset because that value explains 87% of the variability. Analyzing the results, it is possible to infer that the proportion of the area of each type of slab and the daily work performed by a construction worker at a primary duty level best defines the type of slab, because these factors have the highest absolute eigenvector. In that sense, this feature is used to build the vector (Table 16) of the AHP method. The same process was applied to the lowest waste generation based on the number of materials used for each slab type, with four features being analyzed for the application of PCA: form area and the rates per square meter of concrete, steel, and prestressed steel. In this category, three principal components were used for the dataset because that value explains 87.20% of the variability. Analyzing the results, it is possible to infer that the rate per square meter of concrete best defines the type of slab because this has the highest absolute eigenvector. In that sense, this is the feature used to build the vector (Table 17) of the AHP method. It should be noted that, because they are quantitative measures, consumption rates were used to determine the relative priority. \begin{table}
\begin{tabular}{c c} \hline
**Alternatives** & **Productivity** \\ \hline Slab on beams & 0.16835 \\ One-way waffle slab & 0.14970 \\ Two-way waffle slab & 0.20791 \\ Flat slab & 0.19356 \\ Flat waffle slab & 0.28048 \\ \hline \end{tabular}
\end{table} 
Table 16: Productivity criterion priority vector. \begin{table}
\begin{tabular}{c c} \hline
**Alternatives** & **Structural Performance** \\ \hline Slab on beams & 0.19528 \\ One-way waffle slab & 0.18711 \\ Two-way waffle slab & 0.26022 \\ Flat slab & 0.17730 \\ Flat waffle slab & 0.18010 \\ \hline \end{tabular}
\end{table} 
Table 14: Structural performance criterion priority vector. \begin{table}
\begin{tabular}{c c} \hline
**Alternatives** & **Cost** \\ \hline Slab on beams & 0.18868 \\ One-way waffle slab & 0.20280 \\ Two-way waffle slab & 0.20187 \\ Flat slab & 0.19447 \\ Flat waffle slab & 0.21218 \\ \hline \end{tabular}
\end{table} 
Table 15: Cost criterion priority vector. Once the normalized matrix and the priority vectors are obtained for each criterion, it is possible to perform calculations to obtain a unified matrix with all these vectors, as shown in Table 18, where C1--structural performance, C2--productivity/constructability, C3--cost, C4--appearance, C5--waste generation, C6--thermal/acoustic comfort. To obtain the correct reading of the table, a comparison of the alternative must be considered (lines 2-6) with the criterion (columns 2-7). Finally, the composite priorities were calculated by multiplying the preferences by the average of the criteria. The result is presented in Table 19.  
Based on the priority vector, a hierarchy of the slabs can be established, with the slabs ranked from those most-preferred by the specialists to the least-preferred slabs, as illustrated in Figure 8.  
Figure 8: Final slab hierarchy. \begin{table}
\begin{tabular}{c c} \hline \hline
**Alternatives** & **Productivity** \\ \hline Slab on beams & 0.16402 \\ One-way waffle slab & 0.24960 \\ Two-way waffle slab & 0.27237 \\ Flat slab & 0.14926 \\ Flat waffle slab & 0.16475 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Waste generation criterion priority vector. \begin{table}
\begin{tabular}{c c} \hline \hline
**Alternatives** & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** \\ \hline Slab on beams & 0.19528 & 0.16835 & 0.18868 & 0.40291 & 0.16402 & 0.39789 \\ One-way waffle slab & 0.18711 & 0.14970 & 0.20280 & 0.18563 & 0.24960 & 0.12917 \\ Two-way waffle slab & 0.26022 & 0.20791 & 0.20187 & 0.14219 & 0.27237 & 0.12352 \\ Flat slab & 0.17730 & 0.19356 & 0.19447 & 0.09037 & 0.14926 & 0.11086 \\ Flat waffle slab & 0.18010 & 0.28048 & 0.21218 & 0.05370 & 0.16475 & 0.05692 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Relative priority vectors of the criteria.