## 8 Concluding Remarks  
The criticisms to GDM-MOP approaches discussed in the introduction have been basically overcome. To our knowledge, this paper has presented one of the most comprehensive approaches to group multi-objective optimization under imperfect information. Its remarkable generality is supported by several important features: (a) some group members may be compatible with an outranking model of preferences, but other ones may feel comfortable with a preference model based on a weighted-sum value function; (b) the use of outranking models allows to handle veto situations, incomparability and intransitive preferences, whereas the value function model is more appropriate for compensatory aggregation of preferences; (c) some (even all) objective values maybe not the same for different group members; (d) group members may consider their own set of objective functions and constraints; (e) objective values may be imprecise or uncertain; (f) imperfect information on available resources and requirements may be handled; and (g) each group member may have their own perception about the availability of resources and the requirement of resources per activity. It should be remarked that, although the problem was formulated in terms of maximization with resource constraints as in project portfolio optimization, the extension of the method to other formulations is straightforward. Another important feature is related to the definition of what a satisfied group member is. Unlike other group decision making approaches, that definition is independent of the satisfaction stage of other group members. In this paper, the group members' stage of satisfaction/dissatisfaction is assigned by using multi-criteria ordinal classification approaches. These assignments fulfill several consistency properties whose theoretical proofs have been provided by the paper. The level of group satisfaction is represented by a bi-objective measure containing the number of group members who are satisfied/dissatisfied with each particular solution. Taking as bases (i) a limiting boundary (set by each group member) between classes \"satisfactory\" and \"unsatisfactory\", (ii) an outranking/preference relation, and (iii) an algorithm able to optimize the bi-objective measure of satisfaction/dissatisfaction, the method is capable of finding (within the decision variable space) the highest group satisfaction related to each particular stage of the consensus reaching process. The whole approach is based on seven reasonable assumptions. The first two assumptions are common to both models of preferences (outranking and weighted-sum function). Assumptions 3-5 support the outranking model, whereas Assumptions 6-7 are basic for the functional model. Assumptions 4 and 7 show only a very slight difference; Assumptions 3 and 6 play the same role in each model of multi-criteria preferences. In our approach, a good consensus is associated with a high level of satisfaction and a very low level of dissatisfaction. If the bi-objective measure of collective satisfaction/dissatisfaction is not judged as sufficiently close to the desired consensus level, then the group should perform an additional consensus round in which preference parameters, judgments, beliefs, and attitudes facing imperfect knowledge, should be closed. If, after several consensus rounds, the bi-objective measure of collective satisfaction/dissatisfaction does not reach the desired consensus level, the group (or the group moderator) should make a final decision among the different non-dominated solutions in the space of satisfaction/dissatisfaction. To reach high consensus levels requires collaborative attitudes from the group members; this is frequent in project portfolio optimization since the individual DMs represent the common organizational interest. However, as a consequence of the independence of judgments about satisfaction/dissatisfaction, the method can work even in cases of very conflicting views from the individual DMs, helping to identify the best possible partial consensus.