Aggregation in the analytic hierarchy process: Why weighted geometric mean should be used instead of weighted arithmetic mean

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15210%2F18%3A73589021" target="_blank" >RIV/61989592:15210/18:73589021 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0957417418303981" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0957417418303981</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.eswa.2018.06.060" target="_blank" >10.1016/j.eswa.2018.06.060</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Aggregation in the analytic hierarchy process: Why weighted geometric mean should be used instead of weighted arithmetic mean

Popis výsledku v původním jazyce

The main focus of this paper is the aggregation of local priorities into global priorities in the Analytic Hierarchy Process (AHP) method. We study two most frequently used aggregation approaches - the weighted arithmetic and weighted geometric means - and identify their strengths and weaknesses. We investigate the focus of the aggregation, the assumptions made on the way, and the effect of different normalizations of local priorities on the resulting global priorities and their ratios. We clearly show the superiority of the weighted geometric mean aggregation over the weighted arithmetic mean aggregation in AHP for the purpose of deriving global priorities of alternatives. We also contribute to the literature on rank reversal in AHP. In particular, we show that a change of the normalization condition for the local priorities of alternatives may result in different ranking when the weighted arithmetic mean aggregation is used for deriving global priorities of alternatives, and we demonstrate that the ranking obtained by the weighted geometric mean aggregation is not normalization dependent. Moreover, we prove that the ratios of global priorities of alternatives obtained by the weighted geometric mean aggregation are invariant under the normalization of local priorities of alternatives and weights of criteria. We also propose three alternative approaches to aggregating preference information contained in local pairwise comparison matrices of alternatives into a global consistent pairwise comparison matrix of alternatives and prove their equivalence.

Název v anglickém jazyce

Aggregation in the analytic hierarchy process: Why weighted geometric mean should be used instead of weighted arithmetic mean

Popis výsledku anglicky

The main focus of this paper is the aggregation of local priorities into global priorities in the Analytic Hierarchy Process (AHP) method. We study two most frequently used aggregation approaches - the weighted arithmetic and weighted geometric means - and identify their strengths and weaknesses. We investigate the focus of the aggregation, the assumptions made on the way, and the effect of different normalizations of local priorities on the resulting global priorities and their ratios. We clearly show the superiority of the weighted geometric mean aggregation over the weighted arithmetic mean aggregation in AHP for the purpose of deriving global priorities of alternatives. We also contribute to the literature on rank reversal in AHP. In particular, we show that a change of the normalization condition for the local priorities of alternatives may result in different ranking when the weighted arithmetic mean aggregation is used for deriving global priorities of alternatives, and we demonstrate that the ranking obtained by the weighted geometric mean aggregation is not normalization dependent. Moreover, we prove that the ratios of global priorities of alternatives obtained by the weighted geometric mean aggregation are invariant under the normalization of local priorities of alternatives and weights of criteria. We also propose three alternative approaches to aggregating preference information contained in local pairwise comparison matrices of alternatives into a global consistent pairwise comparison matrix of alternatives and prove their equivalence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50202 - Applied Economics, Econometrics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

EXPERT SYSTEMS WITH APPLICATIONS

ISSN

0957-4174

e-ISSN

—

Svazek periodika

114

Číslo periodika v rámci svazku

30. December 2018

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

97-106

Kód UT WoS článku

000446949300008

EID výsledku v databázi Scopus

2-s2.0-85050482086