# Integrated Decision Support Framework of Optimal Scaffolding System for Construction Projects
## 4 Discussion
### Comparisons of Different MCDM Methods  
To compare the assessment results from different MCDM methods, another two methods, including the MAVT (Multi-Attribute Value Theory) and VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje), were applied.  
First, the correlation coefficient values between different methods, which indicate the degree of the ranking changes among the alternatives, were further compared. Table 8 illustrates the correlation coefficients of ranking results from each two methods. It can be concluded that there is a high level of consistency among the ranking results from three methods. Specifically, the correlation coefficient between TOPSIS and VIKOR achieved the highest value of 1.0, which indicates that the ranking results from these two methods are the same. Furthermore, TOPSIS and MAVT also achieved a high value of 0.900, which means the ranking results from MAVT have a strong correlation with TOPSIS.  
Second, to compare the sensitivity results from three MCDM techniques, the sensitivity coefficients were also determined, which reflect the number of changes in the ranking result (single, double or more changes) when the weight of one of the criteria increases or decreases by 5 or 50%. If the ranking results are not changed, the sensitivity coefficient equals 0. If the ranking of one alternative increases and the ranking of another alternative decreases, the sensitivity coefficient equals 2. Table 9 shows the obtained values of sensitivity coefficient (\(SC^{*}\)) when adjusting one criteria weight in different MCDM methods. Specifically, when the weight of each criterion increased or decreased by 5%, there were no changes in the ranking results using different MCDM methods. Furthermore, when the weight decreased by 50%, TOPSIS had the most significant change, and MAVT and VIKOR had a slight change in the ranking. On the other hand, when the weight increased by 50%, TOPSIS also had the most significant change and VIKOR had a slight change while MAVT showed a relatively stable ranking result. This indicates that the results from the TOPSIS method are more sensitive to the weight value changes of the criteria.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **FAHP-TOPSIS** & **FAHP-MAVT** & **FAHP-VIKOR** \\ \hline FAHP-TOPSIS & 1.0 & 0.900 & 1.0 \\ FAHP-MAVT & 0.900 & 1.0 & 0.900 \\ FAHP-VIKOR & 1.0 & 0.900 & 1.0 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Values of correlation coefficient.  
Figure 9: Criteria sensitivity to the weight changes.  
To summarize, as there are a set of conflicting criteria in relation to site conditions, productivity, safety and financial factors, the MCDM methods have the advantage in assessing and ranking the performance of different alternatives. The results show that FAHP-TOPSIS, as well as FAHP-MAVT and FAHP-VIKOR, are effective measurement techniques for ranking the scaffolding systems. The ranking results and the sensitivity analysis from three methods show a high level of similarity among each two methods, which indicates that TOPSIS has a high accuracy in generating the optimal solution. Considering accuracy, simplicity, capability of dealing with each kind of comparison judgment, and the flexibility of the application, this paper adopted the FAHP-TOPSIS as a suitable method in the proposed decision support system regarding the scaffolding type selection problem.