## 6 Summary of the Method
According to Assumption 2, each group member obtains their best compromise solution by solving Problem 11. 5. Each DM sets their limiting boundary in correspondence to Assumption 4 (when the DM is compatible with the outranking model) and Assumption 7 (for DMs compatible with the functional model). 6. Applying the classification models of Sections 4 and 5, the moderator finds non-dominated solutions (\(N_{sat}\), \(N_{dis}\)) of Problem 1. 7. **If there is no solution of good agreement**, further discussions in each subgroup are needed to close divergent beliefs, preference parameters, and constraint settings. We need to update these data. 8. The DMs should judge whether, given the updated data, they want to modify their limiting boundary. In the case of \"yes\", restart the process in Step 5. In the case of \"no\", restart the process in Step 6. **If a good consensus (\(N_{sat}\), \(N_{dis}\))* is found, then:**
9. If the pre-image of (\(N_{sat}\), \(N_{dis}\))* is a single point in the decision variables space, this point corresponds to the best consensus, and the process finishes. **Eise:**
10. Apply some additional criterion to select a single pre-image of (\(N_{sat}\), \(N_{dis}\))*. The process finishes. The method is based on seven assumptions. Table 1 summarizes the set of assumptions and their role within the approach. All the DMs should accept Assumptions 1 and 2. DMs who are compatible with the outranking model should agree to Assumptions 3-5, whereas the other DMs should accept Assumptions 6 and 7. **Remark 7**. :
1. _In the case of project portfolio optimization, the computational cost depends mainly on Step 4. The computational complexity of this step is linear with respect to the number of applicant projects (see the description of the I-NOSGA algorithm in Appendix A)._
2. _Handling group interactions in Steps 1, 2, and 7 is the main difficulty to extend the proposal to problems with many DMs. In such problems, Steps 3, 4, 5, and 8 should be performed by each DM in an independent and parallel way. Parallel processing in Step 4 is strongly recommended. Steps 9 and 10 are independent of the number of group members. The computational effort in Step 6 is, at most, proportional to the number of DMs (see Appendix C). Therefore, with some modifications in Steps 1, 2, and 7, the proposal can be used in large-scale GDM-MOPs. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **It’s Subject** & **Allows** & **Related to** \\ \hline Assumption 1 & Interval numbers as model of imprecisions & Modeling imprecision & Steps 1–2 \\ Assumption 2 & Capacity to identify the best compromise & Identifying best compromises & Step 4 \\ Assumption 3 & Compatibility with an outranking model & Preference modeling & Step 1 \\ Assumption 4 & Capacity to set the limiting boundaries related & Identifying limiting boundaries & Step 5 \\ Assumption 5 & Compatibility with INTERCLASS-nB & Assigning solutions to classes of & Step 6 \\ Assumption 6 & Compatibility with an interval value function & Preference modeling & Step 1 \\ Assumption 7 & Capacity to set the limiting boundaries related & Identifying limiting boundaries & Step 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of assumptions. _._
3. _In Step 7, in order to accept a solution as a good consensus, the group may agree previously appropriate values of_ \(N_{\text{sat}}\) _and_ \(N_{\text{dis}}\) _to represent what a strong majority and a weak minority mean, respectively._
4. _In Step 10, there could be several (even many) pre-images of the best consensus (_\(N_{\text{sat}}\)_,_ \(N_{\text{dis}}\)_)\". To choose a single one, the group and/or its moderator can use different points of view (e.g., impacts of the solutions, resource consumption, who are the satisfied and dissatisfied DMs, number of supported projects in case of portfolio optimization, etc.).