## 8 Concluding Remarks
During discussions and exchange of opinions, the group members should report their real preferences and beliefs. There is no way to manipulate the consensus solution maliciously by declaring insincere preferences and beliefs. The present proposal is capable of modeling priorities on the set of group members; when the moderator has sufficient authority, (s)he can weigh the different non-dominatedsolutions (group satisfaction, group dissatisfaction) according to who are the satisfied and dissatisfied group members. The method (with both models of preferences) behaved well in an illustrative group many-objective project portfolio optimization problem. For simplicity, we used the same parameters for both models, what is a rough approximation since the weights have different meanings. The ideal consensus was achieved with a single consensus round. There is no obstacle to the combined use of both preference models. Another interesting feature of our approach is its potential to handle large scale GDM-MOPs. If parallel processing is used in solving Problem 11, the computational cost of the proposal depends weakly on the number of DMs (see Remark 7.ii in Section 6). With only minor changes, the method could be adapted to handle such optimization problems as an avenue of future research. Other directions for future research are the following:  
* Since consensus is affected by intense (dis)satisfaction, we require to model also high satisfaction and strong dissatisfaction. This could be addressed by multi-criteria ordinal classification methods, but the model would be more complex due to the increment of classes. * Development of models for making an appropriate selection of the best consensus among non-dominated solutions of Problem 1. Logic-based models representing predicates like \"a strong majority is satisfied with... \" and \"a very weak minority disagrees with... \" may be used to select one of the non-dominated solutions in the space of collective satisfaction/dissatisfaction. This would permit to reduce, perhaps replace, the role of the moderator in choosing the final decision. These models should be able to reflect intense satisfaction and dissatisfaction from the group members. * To alleviate the DM hard cognitive task in assessing limiting boundaries, this is more relevant as the numbers of objective functions and DMs increase. Conceptualization, E.F., L.C.-R. and N.R.-V.; methodology, E.F., C.G.-S., N.R.-V. and L.C.-R.; software, N.R.-V. and C.G.-S.; validation, E.F., L.C.-R., N.R.-V. and C.G.-S.; formal analysis, E.F., L.C.-R., C.G.-S.; investigation, L.C.-R., E.F., N.R.-V. and C.G.-S.; writing--original draft preparation, E.F., C.G.-S. and N.R.-V.; writing--review and editing, C.G.-S., L.C.-R., E.F. and N.R.-V. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The instances and other files used here are available at [[https://www.dropbox.com/s/t80u9](https://www.dropbox.com/s/t80u9) kbdcub6 jua/Projects%20 Description.pdf?dl=0]([https://www.dropbox.com/s/t80u9](https://www.dropbox.com/s/t80u9) kbdcub6 jua/Projects%20 Description.pdf?dl=0) (accessed on 12 May 2021). Authors thanks to CONACYT for supporting the projects from (a) Catedras CONACYT Program with Number 3058. (b) CONACYT Project with Number A1-S-11012 from Convocatoria de Investigacion Cientifica Basica 2017-2018 and CONACYT Project with Number 312397 from Programa de Apoyo para Actividades Cientificas, Tecnologicas y de Innovacion (PAACTI), (c) CONACYT Project with Number 236154 and (d) CONACYT Project with Number 280081. The authors declare no conflict of interest. The I-NOSGA algorithm was proposed by [PERSON] et al. (2019). Using an outranking relation, this method identifies non-strictly outranked portfolios (modeled using interval mathematics) during the evolutionary search, satisfying a set of constraints that can be described by intervals. In the present paper, we use a variant of the original algorithm.