Analytic Hierarchy Process (AHP) is a Multi Criteria Decision Making method, originally developed by Prof. Thomas L. Saaty, to rank alternative options and derive ratio scales from paired comparisons.

For each comparison between two options a judgement on how much an element (on the row of the comparison matrix) is more important than an other one (on the column) has to be provided.

Here is a possible interpretation for the assigned values:

9 | extremely more important |

7 | much more important |

5 | more important |

3 | slightly more important |

1 | equally important |

2, 4, 6 and 8 suggest intermediate interpretations and the reciprocals (1/9, 1/8, ...) indicate that the column element is more important than the one on the row (implying that the latter is the less important).

Priorities are calculated based in the eigenvalue approach by the implementation of the

*power method*, a numerical procedure to calculate the maximal eigenvector [Han Xuli, 1997]. This is done by the javascript included in this page, there are no external files, so it can be saved and used offline.

At the end f the task, consistency indicators are also provided: a judgement is said to be consistent if the Consistency Ratio (CR) is lesser than 0.10, otherwise it may be necessary to re-enter the comparison matrix correcting some of its values.

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author: emanuele f.m.

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version: 1.2 [01.2010]

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