## 4 Safety and Sustainability Assessments of U-Shaped Stair Projects: A Case Study
### Criteria WEIGHTS Determination Using Integrated AHP-MEREC Approach

Table 5: Decision matrix \(D\), constructed for the comparison of safety and sustainability of U-shaped interior-staircase projects A1–A9. Finally, normalized E\({}_{j}\) values were determined as MEEC weights. They are presented in Table 9, as well as the subjective AHP weights. The integrated AHP-MEREC weights for all criteria that impact stair safety and sustainability were calculated by applying Equation (6). Table 9 shows that safety and sustainability of the stair projects are mostly impacted by criteria c\({}_{3}\) (intermediate landings) and c\({}_{5}\) (rise height and tread width). The importance of natural lighting (c\({}_{7}\)) was rated as the lowest. According to experts, the importance of natural lighting is relatively low, since natural lighting is not always possible. In such cases, artificial lighting can be installed to maintain optimal lighting levels. However, the experts also agreed that natural lighting should be considered as a more sustainable option, compared to artificial lighting. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & A1 & A2 & A3 & A4 & A5 & A6 & A7 & A8 & A9 \\ \hline c\({}_{1}\) & 0.968 & 0.000 & 1.347 & 1.347 & 0.000 & 0.968 & 0.968 & 1.347 & 0.000 \\ \hline c\({}_{2}\) & 0.414 & 0.782 & 1.305 & 0.000 & 1.305 & 0.000 & 0.414 & 0.782 & 0.414 \\ \hline c\({}_{3}\) & 7.601 & 0.000 & 8.294 & 8.006 & 0.000 & 6.908 & 8.006 & 8.294 & 8.006 \\ \hline c\({}_{4}\) & 1.099 & 1.609 & 0.000 & 0.000 & 1.099 & 1.609 & 1.609 & 0.000 & 1.099 \\ \hline c\({}_{5}\) & 8.987 & 0.000 & 8.006 & 7.601 & 0.000 & 8.006 & 8.006 & 0.000 & 7.601 \\ \hline c\({}_{6}\) & 1.163 & 0.000 & 0.615 & 1.163 & 0.615 & 0.000 & 0.615 & 1.163 & 0.000 \\ \hline c\({}_{7}\) & 0.166 & 0.000 & 0.089 & 0.249 & 0.389 & 0.186 & 1.244 & 1.244 & 1.244 \\ \hline \(S_{i}\) & 1.365 & 0.294 & 1.337 & 1.288 & 0.397 & 1.260 & 1.381 & 1.041 & 1.287 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Overall performance \(S_{i}\) of the alternatives, calculated using Equation (4). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & A1 & A2 & A3 & A4 & A5 & A6 & A7 & A8 & A9 & E\({}_{j}\) \\ \hline c\({}_{1}\) & 0.036 & 0.000 & 0.052 & 0.055 & 0.000 & 0.040 & 0.035 & 0.070 & 0.000 & 0.288 \\ \hline c\({}_{2}\) & 0.015 & 0.087 & 0.050 & 0.000 & 0.134 & 0.000 & 0.015 & 0.040 & 0.016 & 0.358 \\ \hline c\({}_{3}\) & 0.325 & 0.000 & 0.373 & 0.379 & 0.000 & 0.328 & 0.339 & 0.542 & 0.379 & 2.665 \\ \hline c\({}_{4}\) & 0.041 & 0.188 & 0.000 & 0.000 & 0.112 & 0.067 & 0.059 & 0.000 & 0.044 & 0.512 \\ \hline c\({}_{5}\) & 0.398 & 0.000 & 0.357 & 0.356 & 0.000 & 0.392 & 0.339 & 0.000 & 0.356 & 2.198 \\ \hline c\({}_{6}\) & 0.043 & 0.000 & 0.023 & 0.047 & 0.061 & 0.000 & 0.022 & 0.060 & 0.000 & 0.257 \\ \hline c\({}_{7}\) & 0.006 & 0.000 & 0.003 & 0.010 & 0.038 & 0.008 & 0.046 & 0.065 & 0.050 & 0.226 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Calculations of the removal effects E\({}_{j}\) for the MEREC criteria-weighting approach. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **AHP** & **MEREC** & **AHP-MEREC Weights** \\ \hline c\({}_{1}\) & 0.106 & 0.044 & 0.021 \\ \hline c\({}_{2}\) & 0.123 & 0.055 & 0.031 \\ \hline c\({}_{3}\) & 0.247 & 0.410 & 0.456 \\ \hline c\({}_{4}\) & 0.071 & 0.079 & 0.025 \\ \hline c\({}_{5}\) & 0.288 & 0.338 & 0.438 \\ \hline c\({}_{6}\) & 0.120 & 0.040 & 0.022 \\ \hline c\({}_{7}\) & 0.045 & 0.035 & 0.007 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: AHP, MEREC and the integrated AHP-MEREC weights for criteria impacting stair safety and sustainability.