AN ORTHOGONAL BASIS FOR COMPUTING A CONSISTENT APPROXIMATION TO A PAIRWISE COMPARISONS MATRIX

Authors
KOCZKODAJ WW ORLOWSKI M
Citation
Ww. Koczkodaj et M. Orlowski, AN ORTHOGONAL BASIS FOR COMPUTING A CONSISTENT APPROXIMATION TO A PAIRWISE COMPARISONS MATRIX, Computers & mathematics with applications, 34(10), 1997, pp. 41-47
Citations number
10
Journal title
Computers & mathematics with applications → ACNP
ISSN journal
08981221
Volume
34
Issue
10
Year of publication
1997
Pages
41 - 47
Database
ISI
SICI code
0898-1221(1997)34:10<41:AOBFCA>2.0.ZU;2-P
Abstract
The algorithm for finding a consistent approximation to an inconsisten t pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclide an metric. An orthogonal basis is introduced in the vector space forme d by the images of consistent matrices. The required consistent approx imation is the orthogonal projection of the transformed matrix onto th is space.