Preferences in Constraint Satisfaction and Optimization

In this case, all PCs will be considered, but some will be more preferred than others. Such concepts can be expressed in either a qualitative or a quantitative way. Preferences and constraints are closely related notions, since preferences can be seen as a form of "tolerant" constraints. For this reason, there are several constraint-based frameworks to model preferences. One of the most general frameworks, based on soft constraints (Meseguer, Rossi, and Schiex 2006), extends the classical constraint formalism to model preferences in a quantitative way, by expressing several degrees of satisfaction that can be either totally or partially ordered. When there are both levels of satisfaction and levels of rejection, preferences are bipolar and can be modeled by extending the soft constraint formalism (Bistarelli et al. 2006). Preferences can also be modeled in a qualitative way (also called ordinal), that is, by pairwise comparisons. In this case, soft constraints (or their extensions) are not suitable.