Traditionally, constraint satisfaction problems (CSP's) [1] are so defined that "all the constraints are satisfied simultaneously." However, this is not always true. Many CSP's in real-life are "soft CSP's," i.e., an assignment of values to the variables is considered to be a solution even if some constraints are violated. Some of the practical CSP's are fuzzy: they are fully satisfied by some value assignments to the variables in the constraint, and they are considered to be "partially" or "less" satisfied, instead of "violated," by some other assignments. Sometimes a real-life CSP may consist of a mixture of hard constraints and soft constraints. In these cases we are required to find assignments that fully satisfy the hard constraints and fully or partially satisfy the soft constraints.
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