DIMACS TR: 2003-34
Preference Modelling
Authors: Meltem Ozturk, Alexis Tsoukias and Philippe Vincke
ABSTRACT
This paper 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 paper. We
start by discussing different reasons for constructing a model or
preference. 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. In section 7, 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 paper with some concluding remarks.
Paper available at ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-34.ps.gz
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