Flexible Constraints and Qualitative Decision in A.I. (Extended Abstract)

87> (d') indicates that C is more satisfied by d than by d'. Hence, like an objective function, a fuzzy constraint rank-orders the feasible decisions. However, contrary to an objective function a fuzzy constraint also models a threshold (represented by the bottom level 0) beyond which a solution will be rejected. In fact, a fuzzy constraint can be viewed as the association of a constraint (defining the support of C) and a criterion which rank-orders the solutions satisfying the constraints. In this interpretive framework, a membership function, is similar to a qualitative utility function, or better, a value function. A soft constraint C' will be looser than another one C if and only if µC µC' , that is, if any solution to C is at least as feasible for C'. In the presence of very loose constraints it is clear that the use of soft constraints can help breaking ties among feasible solutions, just as objective functions do. On the contrary whe