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Preference Modeling Robustness Multicriteria Analysis Operational Research
Preference Modeling Robustness Multicriteria Analysis Operational Research
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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 decision-aid 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.
  1. 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.
  2. (P,Q,I)-structures
    Applications have shown that there often exists an intermediary area, between the indifference and the strict preference, where the decision-maker 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 decision-maker is clearly indifferent (relation I), and the preference threshold, above which the decision-maker 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.
  3. 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.
  4. 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. Quasi-kernels and co-comparability graphs, in particular, are interesting in this context.
  5. 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 four-valued logic (allowing to represent ignorance and conflict) leads to new interesting characterizations of preference models.
  6. 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

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Updated: 2017-03-27