## Appendix A
### The Detailed Results of Applying the Interactive Algorithm for the Second Case Study
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**DMU\({}_{\text{o}}\)**} & \multicolumn{2}{c}{**1 = 1**} & \multicolumn{2}{c}{**1 = 2**} & \multicolumn{2}{c}{**1 = 3**} & \multicolumn{2}{c}{**1 = 4**} & \multicolumn{2}{c}{**1 = 5**} \\ \hline \multirow{5}{*}{DMU\({}_{04}\)} & \multicolumn{2}{c}{\(\text{f}_{\text{I}}^{\text{min}}\)} & \(-2.000\) & \(-3.000\) & 5.000 & 6.000 & 5.000 \\ \cline{2-11}  & \(\text{f}_{\text{I}}^{\text{s}}\) & \(-1.000\) & \(-1.000\) & 8.000 & 8.000 & 8.000 & 8.000 \\ \cline{2-11}  & \(\text{\pi}_{\text{I}}\) & 0.250 & 0.133 & 0.075 & 0.042 & 0.075 \\ \cline{2-11}  & \(\beta_{1}\) & 0.435 & 0.232 & 0.130 & 0.072 & 0.130 \\ \hline \multirow{5}{*}{DMU\({}_{07}\)} & \(\text{f}_{\text{I}}^{\text{min}}\) & \(-2.000\) & \(-3.000\) & 4.000 & 3.000 & 6.000 \\ \cline{2-11}  & \(\text{f}_{\text{I}}^{\text{s}}\) & \(-1.000\) & \(-1.000\) & 8.000 & 8.000 & 8.000 & 8.000 \\ \cline{2-11}  & \(\text{\pi}_{\text{I}}\) & 0.167 & 0.167 & 0.125 & 0.208 & 0.042 \\ \cline{2-11}  & \(\beta_{1}\) & 0.235 & 0.235 & 0.176 & 0.294 & 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table A3: Calculating parameters for three DMUs to compose model 14 of step 1 of STEM (p = 1) in the second case study. As can be seen in the last column of Table 11, all \(\beta_{1}\), \(1=1,\ldots,5\) were not calculable (n.c.) for DMU\({}_{10}\) (because \(\frac{0}{0}\) occurs in calculating \(\beta_{1}\), \(1=1,\ldots,5\)). So, composing non-radial FDH model 14 for the second iteration of step 2 of STEM for DMU\({}_{10}\) was not possible. This means that the best compromise solution for DMU\({}_{10}\) could not be obtained. As DM suggested no new target for DMU\({}_{10}\) in restarting the second interactive stage, no target existed in FDH model for DMU\({}_{10}\) according to [PERSON]'s opinion, M\({}^{\prime}\) = M\({}^{\prime}\) - DMU\({}_{10}\) (M\({}^{\prime}\) = \(\{\)DMU\({}_{04}\), DMU\({}_{07}\)}). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**DMU\({}_{0}\)**} & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**i or r**} & \multicolumn{2}{c}{\(\phi_{1}^{*}\) or \(\varphi_{r}^{*}\)} & \multicolumn{2}{c}{**f\({}_{1}\)**} & \multicolumn{2}{c}{**Unsatisfied f\({}_{1}\)**} & \multicolumn{2}{c}{**Target**} & \multirow{2}{*}{\(\Delta_{\text{f}_{1}}\)} & \multirow{2}{*}{\(\beta_{1}\)} \\ \hline \multirow{8}{*}{DMU\({}_{04}\)} & 1 & i = 1 & 0.500 & \(-\)1.000 & 0 & 2.000 & \(-\)1.000 & 0.000 \\ \cline{2-8}  & 2 & i = 2 & 0.200 & \(-\)1.000 & 0 & 3.000 & \(-\)2.000 & 0.000 \\ \cline{2-8}  & 3 & r = 1 & 1.600 & 8.000 & 0 & 6.000 & 2.000 & 0.000 \\ \cline{2-8}  & 4 & r = 2 & 1.167 & 7.000 & 1 & 8.000 & \(-\)1.000 & 1.000 \\ \cline{2-8}  & 5 & r = 3 & 1.600 & 8.000 & 0 & 7.000 & 1.000 & 0.000 \\ \hline \multirow{8}{*}{DMU\({}_{07}\)} & 1 & i = 1 & 0.333 & \(-\)1.000 & 0 & 2.000 & \(-\)1.000 & 0.000 \\ \cline{2-8}  & 2 & i = 2 & 0.250 & \(-\)1.000 & 0 & 3.000 & \(-\)2.000 & 0.000 \\ \cline{1-1} \cline{2-8}  & 3 & r = 1 & 2.000 & 8.000 & 0 & 6.000 & 2.000 & 0.000 \\ \cline{1-1} \cline{2-8}  & 4 & r = 2 & 2.333 & 7.000 & 1 & 8.000 & \(-\)1.000 & 1.000 \\ \cline{1-1} \cline{2-8}  & 5 & r = 3 & 1.333 & 8.000 & 0 & 7.000 & 1.000 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Calculated parameters through solving step 2 of the STEM model (p = 1) considering two DMUs (the second case study). Then, non-radial FDH model 14 for DMU\({}_{04}\) and DMU\({}_{07}\) was composed for the first iteration of step 2 of STEM. The results of solving model 14 (Step 2 of STEM for p = 2) and DM's opinions about them for DMU\({}_{04}\) and DMU\({}_{07}\) are shown in Table 11. As all objective functions for DMU\({}_{07}\) were satisfied via [PERSON]'s opinions (the value of all targets of unsatisfied row for DMU\({}_{07}\), that are underlined, were zero), the best compromise solution was obtained, \(\mathrm{M^{\prime}}=\mathrm{M^{\prime}}-\mathrm{DMU}_{07}\) (\(\mathrm{M^{\prime}}=\{\mathrm{DMU}_{10}\}\)).