## Appendix A
### The Detailed Results of Applying the Interactive Algorithm for the Second Case Study  
For determination of DMU targets, the interactive algorithm, including two interactive stages (Figure 1), was applied for the second case study. For the determination of efficient DMUs and their targets, the interactive stage was applied. For o = 1,..., 13, parameters \(x_{i0}=x_{ij},i=1,\ 2,j=1,\ldots,13\), and \(y_{i0}=y_{ji},\ r=1,\ 2,\ 3,\ \mathrm{j}=1,\ldots,13\) were defined. Then non-radial FDH model 12 was made for DMUj, \(j=1,\ 1,\ 13\). These non-radial FDH models were solved, and the obtained results shown in Table 1.  
M = [DMU\({}_{01}\), DMU\({}_{06}\)] and m\({}^{\prime}=\{\{\mathrm{DMU}_{02},\ \mathrm{DMU}_{03},\ \mathrm{DMU}_{04},\ \mathrm{DMU}_{05},\mathrm{DMU}_{07},\ \mathrm{DMU}_{08},\ \mathrm{DMU}_{09},\ \mathrm{DMU}_{10},\ \mathrm{DMU}_{11},\ \mathrm{DMU}_{12},\ \mathrm{DMU}_{13}\}\) are defined with consideration to Table 1. Then DMU\({}_{10}\) Target \(=\{\mathrm{DMU}_{j}\}\), was also defined. To apply the second interactive stage, the pay-off table for non-proceed DMUs was constructed. As M\({}^{\prime}\
eq\varnothing\) (M\({}^{\prime}\) has 11 members), the algorithm should be continued (to find targets of M\({}^{\prime}\) set). Targets of all members of M\({}^{\prime}\) should be determined individually. Suppose that only DMU\({}_{04}\), DMU\({}_{7}\), and DMU\({}_{10}\) were non-proceed DMUs that defined their targets as desired. Therefore, suppose M\({}^{\prime}\) = {DMU\({}_{04}\), DMU\({}_{07}\), DMU\({}_{10}\)} (a sample DMU in cases 2-4 in Table 14). Also suppose that the finding process of DMUs targets were carried out simultaneously, and \((\mathrm{DMU}_{\mathrm{o}}=\mathrm{DMU}_{04},\ \mathrm{DMU}_{7},\ \mathrm{DMU}_{10})\). At first, \(x_{i0}=x_{ij},i=1,\ 2,\ \mathrm{j}=1,\ldots,13\), and \(y_{i0}=y_{ji},r=1,\ 2,\ 3,\ \mathrm{j}=1,\ldots,13\) were defined for DMU\({}_{o}\), o = 4, 7, and 10. Then the pay-off tables (Table 2) were created by composing and solving non-radial model 13 for f\({}_{i}\)(u), 1 = 1,..., 5. N = 13, m = 2 and s = 3 were considered for each DMU\({}_{o}\) in model 13. The calculation and decision phases of STEM were then applied. Finding the suitable DMUs in feasible region were suitable targets of DMU\({}_{o}\) in which the values of f\({}_{i}\), l = 1,..., 5 were as good as the suggested DMU\({}_{o}\) target by DM. Suppose that DM suggests DMU\({}_{06}\) as the target of DMU\({}_{04}\), DMU\({}_{07}\), and DMU\({}_{10}\). So, suggested targets of DM were considered as DM's opinions for f\({}_{i}\), l = 1,..., 5 for each DMU\({}_{o}\). After that, the first iteration of STEM (p = 1) began. Withrespect to step 1 of STEM, \(\pi_{\text{I}}\), \(1=1,\dots,\) 5 was calculated by Equation (3), and then \(\beta_{1}=\frac{\pi_{\text{I}}}{\sum_{\text{I}=0}^{\infty}\pi_{\text{d}}},1=1, \dots,\) 5 was obtained as seen in Table A3. Then model 14 (Step 1 of STEM for p = 1) was composed for DMU\({}_{04}\), DMU\({}_{07}\), and DMU\({}_{10}\). The results of this model solving and DM's opinions about them are shown in Table A4. As seen in the last column of Table A4, the obtained target through solving of non-radial model 14 (step 1 of STEM (p = 1)) for all DMU\({}_{04}\), DMU\({}_{07}\), and DMU\({}_{10}\) was DMU\({}_{01}\). As described previously, DM suggested DMU\({}_{06}\) as the target of DMU\({}_{04}\), DMU\({}_{07}\), and DMU\({}_{10}\). Therefore, the interactive algorithm should be continued for these DMUs one by one. Here, these three DMUs were considered as DMU\({}_{0}\), simultaneously. As shown in Table A4, the value of f\({}_{\text{I}}\) for DMU\({}_{04}\), DMU\({}_{07}\) and DMU\({}_{10}\) was not satisfied via DM's opinions. Therefore, the obtained solutions for considered DMUs were not the best compromise solutions and composing model 14 (the first iteration of step 2 of STEM) for these three DMUs were required. The required parameters for step 2 of STEM (p = 1) considering DMU\({}_{07}\) and DMU\({}_{10}\) were calculated as shown in Table A5.