On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note

W.W Koczkodaj,F Liu,V.W Marek,J Mazurek,M Mazurek,L Mikhailov,C Özel,W Pedrycz,A Przelaskowski,A Schumann,R Smarzewski,D Strzalka,J Szybowski,Y Yayli

doi:10.1016/j.ijar.2020.05.008

On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note

W.W Koczkodaj, F Liu + Show 12 more

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https://doi.org/10.1016/j.ijar.2020.05.008

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Journal: International Journal of Approximate Reasoning	Publication Date: Jun 12, 2020
Citations: 8

Affiliation: Laurentian University, Guangxi University, University of Kentucky, Silesian University in Opava, Rzeszów University of Technology, University of Manchester, King Abdulaziz University, University of Alberta, Warsaw University of Technology, University of Information Technology and Management in Rzeszow, Military University of Technology in Warsaw, University of Technology, AGH University of Krakow, Ankara University

#Use Of Group Theory #Pairwise Comparisons + Show 4 more

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Abstract

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.

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