Multiple Criteria Decision Analysis - Probabilistic Composition of Preferences, Theory and Applications - page 1

Chapter 1
Multiple Criteria Decision Analysis

Abstract A probabilistic approach to multicriteria decision problems can take in
due account the uncertainty that is inevitably present in preference evaluations.
Translating the preference measurements according to different criteria into prob-
abilities of being chosen as the best alternative has two advantages. First, it makes
comparable preference evaluations that come in entirely different scales. Besides, it
opens probabilistic ways to automatically combine the evaluations according to the
multiple criteria.

Keywords Criterion Multicriteria decision Preference relation

1.1 Preference Relations

The multi-criteria decision problem consists of deriving a unique preference relation
between certain alternatives from evaluations of these alternatives according to a set
of different criteria.
To evaluate alternatives according to a criterion means, by considering some
attribute, to associate a value to each of them. According to each criterion, a
different preference relation can be stated, and the problem is to derive from them a
unique combination of such preference relations.
To establish a preference relation means to rank the alternatives in such a way as
to be able to say if each of them is preferable to each other or not.

1.2 Classes of Decision Problems

A particular class of decision problems is that of choice. Instead of a full ranking,
what is then sought is to determine among the alternatives that which is the best for
a particular purpose. This is a multi-criteria decision problem if there are different
criteria according to which it is possible to compare the alternatives.