## 5 Application of AHP-TOPSIS-2N Method
### Step 13--Ordering the Alternatives in Each Scenario
The result of the pessimistic scenario corroborates those of the optimistic and trend scenarios, where company A5 is the best classified and A2 had the worst results. Based on these results, we can cluster the alternatives in the following groups:  
* Group: 1 alternative A5;
* Group 2: alternatives A1, A3, A4 and A6;
* Group 3: alternative A2. Analyzing the groups, it is observed that the A5 alternative can be selected as the company to be incubated, because it obtained the best ordering in both normalizations for all scenarios analyzed. We emphasize that each scenario presented a distribution of weights of the criteria, which makes the selection of this alternative as the best solution to the proposed problem. Analyzing the results obtained, the alternative A5 presented the best classifications in both standardization processes because it had the best performances in six of the fifteen criteria, including those with the highest weights after analysis by the DM. On the other hand, alternative A2, which obtained the worst ordering, presented the worst performance in eight of the fifteen criteria. Besides, the fact that we analyzed three scenarios (with different weights of criteria for each situation), combined with the two normalizations of the AHP-TOPSIS-2N method provides richer and more robust sensitivity analysis, allowing us to observe the behavior of alternatives in both scenarios. This characteristic gives more transparency to the decision-making process about a complex problem, such as the object of this research. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{6}{c}{**Scenario 2: Optimist**} & \multicolumn{6}{c}{**Scenario 3: Pessimist**} \\ \hline \multicolumn{2}{c}{**Normalization N2**} & \multicolumn{2}{c}{**Normalization N4**} & \multicolumn{2}{c}{**Normalization N2**} & \multicolumn{2}{c}{**Normalization N4**} \\ \hline A5 & 0.6806 & A5 & 0.7214 & A5 & 0.7206 & A5 & 0.6914 \\ A4 & 0.6169 & A1 & 0.6207 & A1 & 0.6367 & A3 & 0.6007 \\ A6 & 0.555 & A6 & 0.5323 & A4 & 0.5757 & A4 & 0.5513 \\ A1 & 0.504 & A3 & 0.5203 & A3 & 0.5245 & A6 & 0.5403 \\ A3 & 0.4887 & A4 & 0.5011 & A6 & 0.4982 & A1 & 0.5311 \\ A2 & 0.4156 & A2 & 0.4502 & A2 & 0.4356 & A2 & 0.4802 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Optimist and pessimist scenarios ordering. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Scenario 1: Trend**} \\ \hline \multicolumn{6}{c}{**Normalization N2**} & \multicolumn{6}{c}{**Normalization N4**} \\ \hline Alternative & D+ & D- & Score & Alternative & D+ & D- & Score \\ A5 & 0.0368 & 0.0879 & 0.7046 & A5 & 0.0748 & 0.2383 & 0.7611 \\ A3 & 0.0591 & 0.0876 & 0.5969 & A1 & 0.1416 & 0.2131 & 0.6007 \\ A1 & 0.0645 & 0.0743 & 0.5354 & A3 & 0.1576 & 0.217 & 0.5793 \\ A4 & 0.0575 & 0.0645 & 0.5284 & A6 & 0.1651 & 0.172 & 0.5103 \\ A6 & 0.0635 & 0.0658 & 0.5087 & A4 & 0.1468 & 0.1517 & 0.5081 \\ A2 & 0.0864 & 0.0614 & 0.4156 & A2 & 0.1972 & 0.1681 & 0.4602 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Ordering trend scenario. It must be highlighted that the final ranking depends on the number of vacancies offered by each business incubator. AHP-TOPSIS 2N always allows DM to go back to previous steps to review key information, perform sensitivity analyzes, assess the impact of project weights and scores, and adjust scales; until it reaches the proper stability for the application of the method.