

Preference Modeling
The starting point of our research in preference modeling is the fact
that the classical model, traditionally used in economy, operations
research, finance, actuarial science and, more generally, in the fields
providing decisionaid tools, rests on strong assumptions (complete
comparability, transitivity, ...) which are not often verified in actual
cases. The main goal of our research is to introduce new and, hopefully,
more realistic models, to axiomatize them and to study their
properties.
 Thresholds structures
In order to take into account the presence of indifference
thresholds, new concepts were introduced in the literature
(semiorder, interval order). We are interested in these structures,
especially their characterizations by easily testable properties, their
matricial and numerical representations and some adjustment and
aggregation problems including these concepts.
 (P,Q,I)structures
Applications have shown that there often exists an intermediary
area, between the indifference and the strict preference, where the
decisionmaker hesitates between both situations or gives
contradictory answers depending on the way the questions are presented
to him. This observation led to the introduction of a preference model
including two distinct thresholds: the indifference threshold, under which
the decisionmaker is clearly indifferent (relation I), and the preference
threshold, above which the decisionmaker has a clear strict preference
(relation P). The intermediary area is considered as a region where he
hesitates (relation Q) between indifference and preference. The properties
of these (P, Q, I)structures, in connection with the conditions which are
imposed on the thresholds; constitute a research subject which extends
the previous one.
 Valued and embedded preferences
The modeling of situations where the preferences are more or less
strong (or reliable, or probable) led to the introduction of valued
(or fuzzy) preference relations. The extension of the properties of
the classical (non valued) preference relations to the valued ones
raises a lot of interesting questions. Moreover, the simultaneous
consideration of several preference levels naturally leads to embedded
preference relations which are sometimes representable by numerical
models including several thresholds, generalizing the (P, Q, I)structures.
 Preferences and graphs
The preference, indifference and incomparability relations can
naturally be represented by graphs (oriented or not, valued or not),
so that graph theory can be useful to study or characterize
the properties of these relations. Quasikernels and cocomparability
graphs, in particular, are interesting in this context.
 Preferences and logic
The hesitation between indifference and preference (as introduced
in the (P,Q,I)structures) is not easily manageable by the classical
Boolean logic. The introduction of a fourvalued logic
(allowing to represent ignorance and conflict) leads to new interesting
characterizations of preference models.
 Preference aggregation
Social choice theory and voting procedures provide concepts and
tools for studying the theoretical background of preference aggregation
methods. More particularly, research has started around the concept of
prudent orders.
Projects
Currently no project in the thematic area.
Publications
Updated: 20170327




