On Graphical Modeling of Preference and Importance
  In recent years, CP-nets have emerged as a useful tool for supporting preference elicitation, reasoning, and representation. CP-nets capture and support reasoning with qualitative conditional preference statements, statements that are relatively natural for users to express. In this paper, we extend the CP-nets formalism to handle another class of very natural qualitative statements one often uses in expressing preferences in daily life - statements of relative importance of attributes. The resulting formalism, TCP-nets, maintains the spirit of CP-nets, in that it remains focused on using only simple and natural preference statements, uses the ceteris paribus semantics, and utilizes a graphical representation of this information to reason about its consistency and to perform, possibly constrained, optimization using it. The extra expressiveness it provides allows us to better model tradeoffs users would like to make, more faithfully representing their preferences. 
R. I. Brafman, C. Domshlak, S. E. Shimony
cs.AI