Editing Constraint satisfaction problem (section)

===Flexible CSPs===
Classic CSPs treat constraints as hard, meaning that they are ''imperative'' (each solution must satisfy all of them) and ''inflexible'' (in the sense that they must be completely satisfied or else they are completely violated). '''Flexible CSP'''s relax those assumptions, partially ''relaxing'' the constraints and allowing the solution to not comply with all of them. This is similar to preferences in [[preference-based planning]]. Some types of flexible CSPs include:
* MAX-CSP, where a number of constraints are allowed to be violated, and the quality of a solution is measured by the number of satisfied constraints.
* [[Weighted constraint satisfaction problem|Weighted CSP]], a MAX-CSP in which each violation of a constraint is weighted according to a predefined preference. Thus satisfying constraint with more weight is preferred.
* Fuzzy CSP model constraints as [[fuzzy logic|fuzzy]] relations in which the satisfaction of a constraint is a continuous function of its variables' values, going from fully satisfied to fully violated.