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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Analytic hierarchy process | 4/5 | https://en.wikipedia.org/wiki/Analytic_hierarchy_process | reference | science, encyclopedia | 2026-05-05T14:37:21.439747+00:00 | kb-cron |
Observe that the priorities on each level of the example—the goal, the criteria, and the alternatives—all add up to 1.000. The priorities shown are those that exist before any information has been entered about weights of the criteria or alternatives, so the priorities within each level are all equal. They are called the hierarchy's default priorities. If a fifth Criterion were added to this hierarchy, the default priority for each Criterion would be .200. If there were only two Alternatives, each would have a default priority of .500. Two additional concepts apply when a hierarchy has more than one level of criteria: local priorities and global priorities. Consider the hierarchy shown below, which has several Subcriteria under each Criterion.
The local priorities, shown in gray, represent the relative weights of the nodes within a group of siblings with respect to their parent. The local priorities of each group of Criteria and their sibling Subcriteria add up to 1.000. The global priorities, shown in black, are obtained by multiplying the local priorities of the siblings by their parent's global priority. The global priorities for all the subcriteria in the level add up to 1.000. The rule is this: Within a hierarchy, the global priorities of child nodes always add up to the global priority of their parent. Within a group of children, the local priorities add up to 1.000. So far, we have looked only at default priorities. As the Analytical Hierarchy Process moves forward, the priorities will change from their default values as the decision makers input information about the importance of the various nodes. They do this by making a series of pairwise comparisons.
== Practical examples == Experienced practitioners know that the best way to understand the AHP is to work through cases and examples. One detailed case study, specifically designed as an in-depth teaching example, is provided as an appendix to this article:
A complex step-by-step example with ten Criteria/Subcriteria and six Alternatives: Buying a family car and Machinery Selection Example. Some of the books on AHP contain practical examples of its use, though they are not typically intended to be step-by-step learning aids. One of them contains a handful of expanded examples, plus about 400 AHP hierarchies briefly described and illustrated with figures. Many examples are discussed, mostly for professional audiences, in papers published by the International Symposium on the Analytic Hierarchy Process.
== Criticisms == The AHP is included in most operations research and management science textbooks, and is taught in numerous universities; it is used extensively in organizations that have carefully investigated its theoretical underpinnings. The method does have its critics. In the early 1990s a series of debates between critics and proponents of AHP was published in Management Science and The Journal of the Operational Research Society, two prestigious journals where Saaty and his colleagues had considerable influence. These debates seem to have been settled in favor of AHP:
An in-depth paper was published in Operations Research in 2001. A 2008 Management Science paper reviewing 15 years of progress in all areas of Multicriteria Decision Making in 2008, the major society for operations research, the Institute for Operations Research and the Management Sciences formally recognized AHP's broad impact on its fields. A 1997 paper examined possible flaws in the verbal (vs. numerical) scale often used in AHP pairwise comparisons. Another from the same year claimed that innocuous changes to the AHP model can introduce order where no order exists. A 2006 paper found that the addition of criteria for which all alternatives perform equally can alter the priorities of alternatives. In 2021, the first comprehensive evaluation of the AHP was published in a book authored by two academics from Technical University of Valencia and Universidad Politécnica de Cartagena, and published by Springer Nature. Based on an empirical investigation and objective testimonies by 101 researchers, the study found at least 30 flaws in the AHP and found it unsuitable for complex problems, and in certain situations even for small problems.
== Rank reversal == Decision making involves ranking alternatives in terms of criteria or attributes of those alternatives. It is an axiom of some decision theories that when new alternatives are added to a decision problem, the ranking of the old alternatives must not change — that "rank reversal" must not occur. There are two schools of thought about rank reversal. One maintains that new alternatives that introduce no additional attributes should not cause rank reversal under any circumstances. The other maintains that there are some situations in which rank reversal can reasonably be expected. The original formulation of AHP allowed rank reversals. In 1993, Forman introduced a second AHP synthesis mode, called the ideal synthesis mode, to address choice situations in which the addition or removal of an 'irrelevant' alternative should not and will not cause a change in the ranks of existing alternatives. The current version of the AHP can accommodate both these schools—its ideal mode preserves rank, while its distributive mode allows the ranks to change. Either mode is selected according to the problem at hand. Rank reversal and AHP are extensively discussed in a 2001 paper in Operations Research, as well as a chapter entitled Rank Preservation and Reversal, in the current basic book on AHP. The latter presents published examples of rank reversal due to adding copies and near copies of an alternative, due to intransitivity of decision rules, due to adding phantom and decoy alternatives, and due to the switching phenomenon in utility functions. It also discusses the Distributive and Ideal Modes of AHP. A new form of rank reversal of AHP was found in 2014 in which AHP produces rank order reversal when eliminating irrelevant data, this is data that do not differentiate alternatives. There are different types of rank reversals. Also, other methods besides the AHP may exhibit such rank reversals. More discussion on rank reversals with the AHP and other MCDM methods is provided in the rank reversals in decision-making page.