## 4 Case Study
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Construction Cost** \\ **(f/m) Minimum** \\ \end{tabular} } & \begin{tabular}{c} **Construction** \\ **Performance (m/day)** \\ \end{tabular} & \begin{tabular}{c} **Landscape** \\ **Integration** \\ **Maximum** \\ \end{tabular} & \
\begin{tabular}{c} **Technical Culture** \\ **and Customs** \\ \end{tabular} &
\begin{tabular}{c} **Preservation and** \\ **Maintenance** \\ **Necessities Minimum** \\ \end{tabular} \\ \hline \(f_{i}\)* & 430 & 2.8 & 0.608 & 0.506 & 0.047 \\ \(f_{i}\)– & 870 & 1.5 & 0.041 & 0.065 & 0.564 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values \(f_{i}\)* and \(f_{i}\)–, applicating step 1 of the viekriterijumsko kompromisno rangiranje (VIKOR) method Source: the authors’ own research. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Alternative**} & \begin{tabular}{c} **Construction** \\ **Cost (f/m)** \\ \end{tabular} & \begin{tabular}{c} **Construction** \\ **Performance (m/Day)** \\ \end{tabular} & \begin{tabular}{c} **Landscape** \\ **Integration** \\ \end{tabular} & \begin{tabular}{c} **Technical Culture** \\ **and Customs** \\ \end{tabular} & \
\begin{tabular}{c} **Preservation and** \\ **Maintenance** \\ **Necessities Minimum** \\ \end{tabular} \\ \hline \hline \end{tabular}
\begin{tabular}{c} Reinforced concrete \\ retaining wall \\ Garden retaining wall \\ Green retaining wall \\ Ríprap retaining wall \\ \end{tabular} & 870 & 1.5 & 0.041 & 0.506 & 0.047 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data and values of alternative for each criterion. Source: the authors’ own research. Matlab(r) software to automate the calculations. The results obtained by VIKOR method are shown in Table 5:  
Minimum value of \(Q\) can be observed for the green wall alternative (see Table 5). Both requirements of the VIKOR method are met: requirement 1, acceptable advantage, and requirement 2, stability of the decision-making process. Therefore, there is a compromise solution for the decision-making problem described here, being the alternative of green wall reinforced with geotetich the one most suitable to the determining criteria. To verify the validity of the method, the VIKOR method is applied for another case varying the importance of the different criteria but keeping the criterion of landscape integration as the most important, with the weight between 0.48 and 0.54. Thus, it is confirmed as compromise solution the typology of the green wall, being the best-ranked option in the classification lists \(Q\), \(S\) and \(R\), although within an ensemble of compromise solutions in which a riprap wall is also included as the second option. When using TOPSIS, the green retaining wall is confirmed as the best-ranked solution, obtaining the following classification: Green retaining wall, \(R_{j}\) = 0.9966; Ripprap retaining wall, \(R_{j}\) = 0.5955; Garden retaining wall, \(R_{j}\) = 0.5227; Reinforced concrete retaining wall, \(R_{j}\) = 0.0034. For project 2, the process followed in the previous case must be repeated, calculating on first place the weight matrix for the selection criteria, by paired comparisons. The weight vector obtained is \(w\) = (0.41; 0.03; 0.26; 0.11; 0.18). The consistency of the comparison matrix has been assessed, obtaining a Consistency Ratio of less than 0.1, being able now to conclude that the assessments made are consistent. In the same way, we complete the decision-making process by calculating the values \(S_{j}\), \(R_{j}\) and \(Q_{j}\) and establishing the classification lists of alternatives, Table 6.  
As a result, a minimum of the \(Q\), \(S\) and \(R\) values for the case of the green wall is obtained, but with similar values to those for riprap wall, from which we deduce that there is not a clear optimal solution, but an ensemble of compromise solutions that can be a solution to the problem in a more or less appropriate form. It is demonstrated this by applying requirement 1, acceptable advantage of the VIKOR method.