The analytic hierarchy process is a decision theory method for ranking alternatives from pairwise comparisons (Saaty 1980). A decision
is decomposed into a hierarchy of goals, criteria, and alternatives. At each level,
judgments are recorded in a positive reciprocal matrix 
,
where 
measures the relative importance of item 
over item 
and 
.
The priority vector 
is commonly obtained by normalizing the positive principal
right eigenvector satisfying
 |
For perfectly consistent comparisons, 
and 
. The excess of 
over the matrix order 
is therefore used to measure inconsistency in the judgments.
Priorities are propagated through the hierarchy to obtain an overall ranking of the
alternatives.
