  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.
