A formal framework for weak constraint satisfaction based on fuzzy sets

Recent work in the field of artificial intelligence has shown that many problems can be represented as a set of constraints on a set of variables, i.e., as a constraint satisfaction problem. Unfortunately, real world problems tend to be inconsistent, and therefore the corresponding constraint satisfaction problems do not have solutions. A way to circumvent inconsistent constraint satisfaction problems is to make them fuzzy. The idea is to associate fuzzy values with the elements of the constraints, and to combine these fuzzy values in a reasonable way, i.e., a way that directly corresponds to the way crisp constraint problems are handled