The AHP method, developed by T.Saaty (Saaty 1980), is based on 3 principles: decomposition, comparative judgments (pairwise
comparisons of criteria, and pairwise comparisons of alternatives against each criterion) and synthesis of priorities:
- Decomposition: AHP hierarchy development (with the use of Value Tree);
- Comparative judgments: pairwise comparisons of criteria, and pairwise comparisons
of alternatives against each criterion (of the lowest level);
- Synthesis of priorities: determination of weights based on pairwise comparison of
criteria (including comparison through hierarchy/Value Tree), and determination of scores (eigenvectors for the maximum eigenvalue;
determination of the overall score using linear additive model.
AHP presents an integration of the additive model (2) with a distinctive determination of the decision matrix, Vi,a,
and criteria weights, wi, i=1,...,m. Within AHP a systematic pairwise comparison of alternatives with respect to each
criterion is used based on a special ratio scale: for a given criterion, alternative i is preferred to alternative j with the
strength of preference given by aij=s, 1 ≤ s ≤ 9, correspondingly, aji=1/s. Then, the same procedure
is implemented for m(m-1)/2 pairwise comparisons in the same scale for m criteria. The obtained matrices are processed
(by extracting the eigenvector corresponding to the maximum eigenvalue of the pairwise comparison matrix) (Belton 2002; Saaty 1980)
and yield the values Vi,a and weights wi for subsequent use with the model, when preferences are aggregated
across different criteria according to (2).
AHP may thus be considered an MAVT approach with a specific elicited value function (scoring) and criteria weights (weighting).
However, taking into account different assumptions and approaches, proponents of AHP insist that it is not a value function method
(Belton 2002). Additionally, AHP relies on the supposition that humans are more capable of making relative judgments than absolute
judgments. Consequently, the rationality assumption in AHP is more relaxed than in MAVT.
AHP popularity is due to its flexibility and ease of use, and availability of software packages (ExpertChoice software; IDRISI GIS
also provides an example of integration of the AHP into GIS-based multicriteria analysis (Eastman, 1993,1997)).
AHP method has not been without criticism:
- ambiguity in the meaning of the relative importance of 1 element of the decision
hierarchy when it is compared to another element;
- the number of comparisons for large problems;
- the use of 1-9 scale.
Some researches argue that the type of questions asked during the process of pairwise comparisons are meaningless (Belton 1986).
Another criticism is related to the rank reversal problem (Belton 1983, Dyer 1990).
Decerns authors recommend using AHP method (if ratio scale within the pairwise comparison is considered by involved experts
as suitable for the problem under investigation) as a preliminary step and only in the cases, when implementation of other
methods seems too/more complicated.