ABSTRACTPartial and fuzzy constraint satisfaction involves finding an assignment of values to the variables that maximally satisfies the given set of constraints. Fuzzy logic is a very suitable mathematical tool for representing and reasoning about constraints that are better viewed as “preferences” than “restrictions,” or that do not have a sharp definition of being satisfied or not. This article presents mathematical definitions of weak consistencies and partial constraint propagation based on fuzzy logic as an extension and generalization of the corresponding notions of consistency and constraint propagation in classical constraint satisfaction problems. The fuzzy logic based approach provides a unifying mathematical framework that allows the same set of techniques and algorithms to be applied to complete, fuzzy and partial constraint satisfaction problems.