Paper Info
Title
On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices
Abstract
The aim of the paper is to obtain some theoretical and numerical properties of Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices (PRM). In the case of 3 脳 3 PRM, a differentiable one-to-one correspondence is given between Saaty's inconsistency ratio and Koczkodaj's inconsistency index based on the elements of PRM. In order to make a comparison of Saaty's and Koczkodaj's inconsistencies for 4 脳 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n 脳 n PRM is formulated, the elements a ij (i j) of which were randomly chosen from the ratio scale $$\dfrac{1}{M}, \dfrac{1}{M-1}, \ldots , \dfrac{1}{2}, 1, 2, \ldots , M - 1, M,$$ with equal probability 1/(2M 驴 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency.
Year
DOI
Venue
2008
10.1007/s10898-007-9236-z
J. Global Optimization
Keywords
Field
DocType
keywords pairwise comparison matrix · inconsistency · inconsistency index · randomly generated pairwise comparison matrix,ratio scale,dimension number increase,dimension number,maximal eigenvalues,pairwise comparison matrix,n prm,different type,inconsistency ratio,average value,1 m,inconsistency index,indexation,mathematics,econometrics,statistical analysis,empirical distribution
Discrete mathematics,Pairwise comparison,Combinatorics,Ratio Scale,Matrix (mathematics),Differentiable function,Asymmetry,Eigenvalues and eigenvectors,Pairwise comparison matrix,Mathematics,Statistical analysis
Journal
Volume
Issue
ISSN
42
2
0925-5001
Citations 
PageRank 
References 
53
3.08
6
Authors
2
Name
Order
Citations
PageRank
Sándor Bozóki115810.98
T. Rapcsák213520.90