On Linguistic Fuzzy Constraint Satisfaction Problems

Fuzzy constraint satisfaction problems (FCSPs) extend standard (crisp) constraint satisfaction problems (CSPs) by introducing a notion of fuzzy constraints. Fuzzy constraints allow one to express the degrees to which the constraints are satisfied with a given instantiation of constrained variables. The main advantage of FCSPs is flexibility in handling the constraints including their representation, satisfaction and relaxation. However, similarly to CSPs, FCSPs consider the variable instantiations in the form of singletons only, i.e. the constrained variables take single, usually numerical, values from their domains. A solution of a FCSP consists of a complete instantiation of all the constrained variables together with a degree of satisfaction of the constraints with the instantiation. In some applications such as decision analysis and support it may be desirable to express possible instantiations and solutions in more qualitative or descriptive way taking into account imprecision and uncertainty of the solutions. A concept of linguistic variable in fuzzy logic and in particular in computing with words has been developed for that purpose and it can also be used in FCSPs to advantage. Linguistic FCSPs (LFCSPs) extend FCSPs by considering the constrained variables as linguistic variables taking linguistic values that are words or sentences in a natural or synthetic language rather then single numerical values. In this paper some aspects of LFCSPs that aim in providing flexibility in handling both constraints and solutions are presented.