Preference Modelling
Résumé
This chapter provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the chapter. We start by discussing different reasons for constructing a preference model. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. We also deal with the problem of how to extend a preference relation over a set A of “objects” to the set of all subsets of A. In Sect. 3.9, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with “compact representation of preferences” introduced for special purposes. We end the chapter with some concluding remarks.