Abstract of my PhD thesis
Additive utility functions are one of the most efficient tools for representing
multi-attribute preferences. This explains why conditions ensuring the existence
of such functions have been thoroughly studied.
In practice, however, cancellation axioms, which are necessary conditions for
additive representability, are very difficult to handle. This led researchers in
the field to replace them by very restrictive, but easy to use, structural
hypotheses on all the dimensions of the preference spaces, hence limiting the
range of application of additive utilities. These so-called hypotheses are
solvability in the algebraic approach and connexity in the topological
approach. The aim of this thesis is to present new conditions, as testable as
the former, but less restrictive.
On one hand, our study of cancellation axioms led to the following result:
testable conditions do not exist without structural hypotheses with respect to
at least two dimensions of the preference space. On the other hand, we managed
to show that such testable conditions exist when at least two of these
dimensions have some structural properties. Since the classical approaches
(i.e., the algebraic and the topological approaches) did not seem well adapted
for reaching this result, we defined a new approach, called the analytic
We illustrate these theoretical results using two examples on which the
classical results fail to apply: (i)~a group decision making, where some
of the attributes are solvable and others are not; (ii)~a decision model based
on imprecise sampled data.
Finally, we designed a graphical application for constructing additive
utility functions. For this purpose, we developed a model based on a
question/answer process, which reduces problems of imprecision and of bias in the
answers of the users.