Solving set-valued constraint satisfaction problems

In this paper, we consider the resolution of constraint satisfaction problems in the case where the variables of the problem are subsets of $${\mathbb{R}^{n}}$$. In order to use a constraint propagation approach, we introduce set intervals (named i-sets), which are sets of subsets of $${\mathbb{R}^{n}}$$ with a lower bound and an upper bound with respect to the inclusion. Then, we propose basic operations for i-sets. This makes possible to build contractors that are then used by the propagation to solve problem involving sets as unknown variables. In order to illustrate the principle and the efficiency of the approach, a testcase is provided.