## 5 Application of AHP-TOPSIS-2N Method
### Step 13--Ordering the Alternatives in Each Scenario  
We applied the AHP-TOPSIS 2N method, considering the three scenarios. To obtain D+, D\(-\) and score (C) values, we applied Equations (7)-(9) respectively. In the trend scenario, the companies were ordered as demonstrated in Table 15. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{
\begin{tabular}{c} **Criteria/** \\ **Alternatives** \\ \end{tabular} }} & \multicolumn{10}{c}{**Criteria**} & \multicolumn{10}{c}{**Weight**} \\ \cline{2-13}  & **Trend** & **Optimist** & **Pessimist** & **Trend** & **Optimist** & **Pessimist** & **Pessimist** \\ \hline \(\text{C}_{1}\) & Technical and Economic Feasibility of the Project & 0.1135 & 0.1007903 & 0.058824 & & & & & & & & & & & & \\ \(\text{C}_{2}\) & Potential of interaction of research activities & 0.0681 & 0.0604742 & 0.050074 & & & & & & & & & & & & \\ \(\text{C}_{3}\) & Technological content & 0.1046 & 0.092887 & & & & & & & & & & & & & \\ \(\text{C}_{4}\) & Innovative Content & 0.0845 & & & & & & & & & & & & & & & \\ \(\text{C}_{5}\) & Sustainability & 0.0549 & & & & & & & & & & & & & & & \\ \(\text{C}_{6}\) & Ability to generate and attract resources & 0.1034 & & & & & & & & & & & & & & & \\ \(\text{C}_{7}\) & Relevance of the problem to be solved & 0.0918 & & & & & & & & & & & & & & & \\ \(\text{C}_{8}\) & Marketing Feasibility & 0.0614 & & & & & & & & & & & & & & & \\ \(\text{C}_{9}\) & Management Feasibility & 0.0444 & & & & & & & & & & & & & & & & \\ \(\text{C}_{10}\) & Current stage of product or process development. & 0.0374 & & & & & & & & & & & & & & & & \\ \(\text{C}_{11}\) & Creativity and originality & 0.0582 & & & & & & & & & & & & & & & & \\ \(\text{C}_{12}\) & Correct filling and clarity of the proposal & 0.0641 & & & & & & & & & & & & & & & & & \\ \(\text{C}_{13}\) & Public policy & 0.0365 & & & & & & & & & & & & & & & & & \\ \(\text{C}_{14}\) & Relationship with local government & 0.0352 & & & & & & & & & & & & & & & & & \\ \(\text{C}_{15}\) & Formed relationship network (Networking) & 0.042 & & & & & & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Weights of criteria. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{
\begin{tabular}{c} **Criteria/** \\ **Alternatives** \\ \end{tabular} }} & \multirow{2}{*}{\(\text{C}_{1}\)} & \(\text{C}_{2}\) & \(\text{C}_{3}\) & \(\text{C}_{4}\) & \(\text{C}_{5}\) & \(\text{C}_{6}\) & \(\text{C}_{7}\) & \(\text{C}_{8}\) & \(\text{C}_{9}\) & \(\text{C}_{10}\) & \(\text{C}_{11}\) & \(\text{C}_{12}\) & \(\text{C}_{13}\) & \(\text{C}_{14}\) & \(\text{C}_{15}\) \\ \hline \(\text{A}_{1}\) & 5 & 5 & 5 & 3 & 3 & 5 & 1 & 3 & 2 & 2 & 3 & 2 & 2 & 2 & 2 \\ \(\text{A}_{2}\) & 5 & 1 & 1 & 1 & 1 & 4 & 3 & 1 & 1 & 1 & 5 & 5 & 5 & 1 & 5 \\ \(\text{A}_{3}\) & 5 & 4 & 5 & 4 & 3 & 3 & 5 & 5 & 3 & 2 & 1 & 2 & 1 & 1 & 1 \\ \(\text{A}_{4}\) & 3 & 4 & 3 & 3 & 2 & 4 & 4 & 4 & 4 & 4 & 1 & 3 & 3 & 3 & 2 \\ \(\text{A}_{5}\) & 5 & 3 & 5 & 3 & 4 & 5 & 4 & 3 & 5 & 4 & 4 & 5 & 5 & 1 & 3 \\ \(\text{A}_{6}\) & 2 & 2 & 4 & 2 & 5 & 5 & 3 & 3 & 3 & 5 & 4 & 3 & 1 & 4 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Scoring of alternatives for each criterion of Incubator X. Company A5 had a better evaluation, with similar results in the two normalizations; we emphasize the scores obtained by this alternative, with a considerable relative difference for the other companies in the two normalizations. Company A2 received the worst evaluations. The other alternatives presented variations in their ordering in both scenarios. Applying the same procedure for calculating the scores, we obtain the Optimist and pessimist scenarios ordering (Table 16). In the optimist scenario, company A2 was also ranked first, but with a smaller relative difference for the other alternatives. In the same way, as in scenario 1, the alternative A2 obtained the worst performance and the other ones presented great variations in scores and ordering.