Approaches to Criteria Combination - Probabilistic Composition of Preferences, Theory and Applications - page 4

Chapter 2
Approaches to Criteria Combination

Abstract Two main approaches to consider the importance of the criteria in a
multicriteria decision may be employed. The preferences according to each of them
may be combined into a global preference by a weighted average where the
importance of the criteria enters separately as weights. Otherwise the interaction
between the evaluations by the multiple criteria must be taken into account when
combining them and the importance of sets of criteria taken together must be
computed. A simple procedure to determine the importance in the

rst case can be
based on pairwise comparison of the criteria. A procedure to compute the impor-
tance of the sets of criteria to apply the Choquet integral in the second case may be
based on pairwise comparison of preferences between distributions of probability
on the space of criteria.

Keywords Weighted average Analytic hierarchy process Pairwise compari-

son Capacity Choquet integral

2.1 Uncertainty About Preferences

The combination of multiple criteria to decide on alternatives of action is a practical
problem that every person could face at any moment. Moreover, at different times,
even if the problem is formulated in the same way, the solution chosen by the same
decision maker may be different. Preference depends on the criteria that are taken
into account, on the importance assigned to each of them, on the relations assumed
between them and, aside from all these and other features of the problem that can be
objectively modeled, on subjective disturbances, which change quickly and cannot
be accurately determined.
Inaccuracy affects even the simplest criteria, based on registering the presence or
absence of traits considered relevant to describe each element of the set of alter-
natives, as in the double-entry tables of Bourdieu ( 1992 ).