On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19520%2F20%3AA0000117" target="_blank" >RIV/47813059:19520/20:A0000117 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0888613X2030178X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X2030178X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ijar.2020.05.008" target="_blank" >10.1016/j.ijar.2020.05.008</a>
Alternative languages
Result language
angličtina
Original language name
On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note
Original language description
This paper examines the constricted use of group theory in the study of pairwise comparisons. The presented approach is based on the application of the celebrated Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multiplicative (ratio) pairwise comparisons is provided. Counterexamples are provided to support the theory. In our opinion, the scientific community must be made aware of the limitations of using the group theory in pairwise comparisons. Groups, which are not torsion free, cannot be used for ratios by Levi's theorems.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA18-01246S" target="_blank" >GA18-01246S: Non-standard optimization and decision-making methods in management processes</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Approximate Reasoning
ISSN
0888-613X
e-ISSN
—
Volume of the periodical
Neuveden
Issue of the periodical within the volume
124
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
7
Pages from-to
59-65
UT code for WoS article
000564641500004
EID of the result in the Scopus database
2-s2.0-85086502353