Logical analysis of fuzzy constraint satisfaction problems

Fuzzy sets naturally model elastic constraints, the fuzzy constraints satisfaction problem (FCSP) enables the introduction of different kinds of flexibility. Levels of priority can be attached to constraints, and satisfaction levels can be fuzzily thresholded. Fuzzy constraints are aggregated by min operation into a fuzzy set membership function to be maximized (discrimin and leximin refinements of the min ordering can be also used in this maximization). This representation framework, originally expressed in terms of membership functions, is equivalently translated into a set of prioritized crisp constraints, in this paper. We take advantage of this representation for modelling aggregations different from min, expressing either reinforcement or compensation. This offers a logical understanding of fuzzy constraints. In relation to this new representation scheme, computational aspects are briefly exemplified and discussed.