Approaches to Criteria Combination - Probabilistic Composition of Preferences, Theory and Applications - page 7

group of evaluators, with the weights corresponding to the importance assigned to
each different evaluator.
A strategy to reach a distribution of weights for the criteria is to ask the decision
maker to compare the criteria pairwise and, afterwards, extract from the results of
these comparisons a probability for the choice of each isolated criteria.
Even establishing preferences between the elements of a pair of criteria is not
free of error. However, limiting the object of each evaluation to a pair and limiting
the set of outcomes of the comparison to a small set of possible results (indifference
of preference for one or another, or a little more in cases where a few different
degrees of preference are employed) presents considerably less dif

culty than

evaluating each criterion directly against some xed pattern.

2.2.1 The Analytic Hierarchy Process

Saaty ( 1980 ) developed an elegant, though laborious, method to find the weights for

the desired criteria as part of a methodology named Analytic Hierarch Process
(AHP). It involves the pairwise comparison of the criteria using a scale of values for
this comparison, with a criterion being at most 9 times more important than any
other.
When performing this pairwise comparison, one must keep in mind that the
effect of the weights depends on the different scales on which the evaluations
according to the two criteria will be measured. Thus, the comparison between the
weights implicitly involves a comparison between these scales. This inner scale
adjustment may be avoided only if the application of all the criteria is conceived in
such a way as to involve the same scale.
To tackle this problem, Saaty proposes to start the modeling by prioritizing
criteria conceived in an abstract form instead of derived from the analysis of the
observed attributes of the alternatives. He nes the criteria and compares

their importance. Arranging the goals, attributes, issues, and stakeholders in a
hierarchy, AHP provides an overall view of the complex relationships inherent to
the situation and helps the decision maker assess whether the issues in each level
are of the same order of magnitude so that he can compare homogeneous elements
accurately (Saaty 1990 ). By this approach, only when the criteria are applied to
compare the alternatives by the values of its attributes do the scales on which these
attributes are effectively measured appear.
A different way to address this problem of scaling is to replace each vector of
attribute measurements that appear naturally with the probabilities of the different
alternatives presenting the best value for such measurements. When establishing, in
the next step, the priorities for the use of each of these vectors of probabilities, we
have, at the same time, values measured on the same scale and conceptual criteria
built on a concrete basis to compare the alternatives. The prioritization of the
criteria thus de

rst de

ned can be made on a sounder basis than if we start from abstract

concepts.