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A Novel Interaction Protocol of a Multiagent System for the Study of Alternative Decisions Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Some Remarks on the Mean-Based Prioritization Methods in AHP

Authors : Konrad Kułakowski, Anna Kȩdzior

Published in: Computational Collective Intelligence

Publisher: Springer International Publishing

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Abstract

EVM (eigenvector method) and GMM (geometric mean method) are probably the two most popular priority deriving techniques for AHP (Analytic Hierarchy Process). Although much has already been discussed about these methods, one frequently repeated question is: what do they have in common? In this paper we show that both these methods can be constructed based on the same principle that the priority of one alternative should correspond to the weighted mean of priorities of other alternatives. We also show how the accepted principle can be used to construct priority deriving methods for the generalized (non-reciprocal) pairwise comparisons matrices.

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previous chapter A Constraint-Based Approach to Modeling and Solving Resource-Constrained Scheduling Problems
next chapter Bi-criteria Data Reduction for Instance-Based Classification
Footnotes
1
The vector associated with the principal eigenvalue (spectral radius) of A.
 
2
Note that accepting \(w(c_{n})=1\), due to (7), we immediately get a solution of (11) in the form \([a_{1n},a_{2n},\ldots ,a_{n-1,n},1]\).
 
3
It is enough to notice that:
$$ \frac{w_{r}}{w_{k}}=\frac{\left( \prod _{j=1}^{n}a_{rj}\right) ^{\frac{1}{n}}}{\left( \prod _{j=1}^{n}a_{kj}\right) ^{\frac{1}{n}}}=\left( \prod _{j=1}^{n}\frac{a_{rj}}{a_{kj}}\right) ^{\frac{1}{n}}=\left( \prod _{j=1}^{n}a_{rj}a_{jr}a_{rk}\right) ^{\frac{1}{n}}=\left( \prod _{j=1}^{n}a_{rk}\right) ^{\frac{1}{n}}=a_{rk} $$
for every \(k,r=1,\ldots ,n\).
 
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Metadata
Title
Some Remarks on the Mean-Based Prioritization Methods in AHP
Authors
Konrad Kułakowski
Anna Kȩdzior
Copyright Year
2016
Book
Computational Collective Intelligence

Print ISBN: 978-3-319-45242-5

Electronic ISBN: 978-3-319-45243-2

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-45243-2_40

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