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Fuzzy modeling of priority and preference in constraint satisfaction problems. (English) Zbl 1028.91526
Summary: In classical Constraint Satisfaction Problems (CSPs), hard constraints restrict the possible values of a set of variables. However, real world constraint problems are often flexible, and classical CSPs are idealizations that do not account for the preference among feasible solutions. Moreover, some constraints may have priority over others. This paper advocates the use of fuzzy set and possibility theory as a realistic approach for the representation of these two aspects: preference relations among possible instantiations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instantiations are provided owing to the relaxation of some constraints.

91B06 Decision theory
03E72 Theory of fuzzy sets, etc.