Specifying fuzzy constraints interactions without using aggregation operators

A tuple of fuzzy constraints defined on a discrete satisfaction scale defines a lattice structure, called relaxation space, made of the tuples of level cuts of the fuzzy constraints, equipped with the partial order induced by the scale ordering. Then choosing a way of combining the fuzzy constraints has two joint effects: usually a completion of the ordering between tuples of levels, and possibly a simplification of the relaxation space (by eliminating subsumed tuples corresponding to the same level of global satisfaction). The paper investigates the possibility of specifying the ordering between tuples of level cuts constraints on a simplified relaxation space, without resorting to the use of explicit aggregation operations. The idea is to elicit the preferences between the tuples of constraints representing various relaxations of the set of fuzzy constraints, directly from the user. The way to express these preferences in a local manner is also discussed.