TY - JOUR

T1 - Deriving weights from general pairwise comparison matrices

AU - Hovanov, Nikolai V.

AU - Kolari, James W.

AU - Sokolov, Mikhail V.

PY - 2008/3/1

Y1 - 2008/3/1

N2 - The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matrices are not reciprocally symmetric. In this paper we employ both statistical and axiomatic arguments to derive weights from such matrices. Both of these approaches lead to geometric mean-type approximations. Numerical comparison of the obtained geometric mean-type solutions with Saaty's eigenvector method is provided also.

AB - The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matrices are not reciprocally symmetric. In this paper we employ both statistical and axiomatic arguments to derive weights from such matrices. Both of these approaches lead to geometric mean-type approximations. Numerical comparison of the obtained geometric mean-type solutions with Saaty's eigenvector method is provided also.

KW - AHP

KW - Consistency

KW - Geometric mean

KW - Pairwise comparison matrices

UR - http://www.scopus.com/inward/record.url?scp=39049152443&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2007.07.006

DO - 10.1016/j.mathsocsci.2007.07.006

M3 - Article

AN - SCOPUS:39049152443

VL - 55

SP - 205

EP - 220

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 2

ER -