Bozóki, Sándor and Rapcsák, Tamás (2008) On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices. Journal of Global Optimization, 42 (2). pp. 157175. ISSN 09255001

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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 3x3 PRM, a differentiable onetoone 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 4x4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated nxn PRM is formulated, the elements aij (i<j) of which were randomly chosen from the ratio scale 1/M, 1/(M1), ... , 1/2, 1, 2, ..., M1, M with equal probability 1/(2M1) and aji is defined as 1/aij. 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.
Item Type:  Article 

Subjects:  H Social Sciences / társadalomtudományok > HB Economic Theory / közgazdaságtudomány H Social Sciences / társadalomtudományok > HB Economic Theory / közgazdaságtudomány > HB5 Mathematical economics / matematikai közgazdaságtan Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra 
Depositing User:  Dr. Sándor Bozóki 
Date Deposited:  11 Sep 2018 12:29 
Last Modified:  11 Sep 2018 12:29 
URI:  http://real.mtak.hu/id/eprint/83501 
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