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 approach.

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.

My PhD thesis (in french) is downloadable here.