Deriving weights from pairwise comparison matrices: The additive case

Jonathan Barzilai; Boaz Golany

doi:10.1016/0167-6377(90)90062-A

Deriving weights from pairwise comparison matrices: The additive case

Jonathan Barzilai, Boaz Golany

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the arithmetic mean.

Original language	English
Pages (from-to)	407-410
Number of pages	4
Journal	Operations Research Letters
Volume	9
Issue number	6
DOIs	https://doi.org/10.1016/0167-6377(90)90062-A
State	Published - Nov 1990

Keywords

arithmetic mean
decision analysis
geometric means
pairwise comparison matrices

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

Access to Document

10.1016/0167-6377(90)90062-A

Cite this

@article{e955b8eeeaa34ece971d85ba5437e174,

title = "Deriving weights from pairwise comparison matrices: The additive case",

abstract = "The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the arithmetic mean.",

keywords = "arithmetic mean, decision analysis, geometric means, pairwise comparison matrices",

author = "Jonathan Barzilai and Boaz Golany",

year = "1990",

month = nov,

doi = "10.1016/0167-6377(90)90062-A",

language = "אנגלית",

volume = "9",

pages = "407--410",

number = "6",

}

TY - JOUR

T1 - Deriving weights from pairwise comparison matrices

T2 - The additive case

AU - Barzilai, Jonathan

AU - Golany, Boaz

PY - 1990/11

Y1 - 1990/11

N2 - The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the arithmetic mean.

AB - The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the arithmetic mean.

KW - arithmetic mean

KW - decision analysis

KW - geometric means

KW - pairwise comparison matrices

UR - http://www.scopus.com/inward/record.url?scp=0025521771&partnerID=8YFLogxK

U2 - 10.1016/0167-6377(90)90062-A

DO - 10.1016/0167-6377(90)90062-A

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0025521771

SN - 0167-6377

VL - 9

SP - 407

EP - 410

JO - Operations Research Letters

JF - Operations Research Letters

IS - 6

ER -

Deriving weights from pairwise comparison matrices: The additive case

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this