10 pagesThe decomposition of a global problem into several sub-problems, that can have antagonist goals, requires to find trade-off solutions. Moreover, the sub-problems are often multi-objective optimization problem: the disciplines have several antagonist objectives to optimize simultaneously. Thus, trade-off solutions have to be found both at the discipline level and at the multidisciplinary level. One way to consider the compromise is to compute all the Pareto efficient solutions of the multi-objective problem involving all the objectives of the disciplines at the same time. The optimal solutions can then be defined as the direct product of each disciplines partial ordered set by Pareto dominance relation. Unfortunately, this definition of the compromise is not satisfying. Indeed, information about efficiency of the solutions inside each discipline is lost during the direct product. In this paper, we propose extensions of the partial ordered set defined by the Pareto dominance relation in each discipline that keeps this information. Another dominance relation over disciplines is also presented
