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

J 2020

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

KOCZKODAJ, W. W., F. LIU, J. MAREK, M. MAZUREK, Jiří MAZUREK et. al.

Basic information

Original name

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

Authors

KOCZKODAJ, W. W. (124 Canada, guarantor), F. LIU, J. MAREK (840 United States of America), M. MAZUREK (616 Poland), Jiří MAZUREK (203 Czech Republic, belonging to the institution), L. MIKHAILOV (826 United Kingdom of Great Britain and Northern Ireland), C. ÖZEL, W. PEDRYCZ (124 Canada), A. PRZELASKOWSKI (616 Poland), A. SCHUMANN (616 Poland), R. SMARZEWSKI (616 Poland), D. STRZALKA (616 Poland), J. SZYBOWSKI (616 Poland) and Y. YAYLI

Edition

International Journal of Approximate Reasoning, Amsterdam, Nizozemí, Elsevier, 2020, 0888-613X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

RIV identification code

RIV/47813059:19520/20:A0000117

Organization unit

School of Business Administration in Karvina

DOI

http://dx.doi.org/10.1016/j.ijar.2020.05.008

UT WoS

000564641500004

Keywords in English

Pairwise comparisons; Inconsistency; Approximate reasoning; Group theory

Links

GA18-01246S, research and development project.

Změněno: 21/4/2021 09:31, Miroslava Snopková

Abstract

V originále

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.

Citovat

KOCZKODAJ, W. W., F. LIU, J. MAREK, M. MAZUREK, Jiří MAZUREK, L. MIKHAILOV, C. ÖZEL, W. PEDRYCZ, A. PRZELASKOWSKI, A. SCHUMANN, R. SMARZEWSKI, D. STRZALKA, J. SZYBOWSKI and Y. YAYLI. On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note. International Journal of Approximate Reasoning. Amsterdam, Nizozemí: Elsevier, 2020, Neuveden, No 124, p. 59-65. ISSN 0888-613X. Available from: https://dx.doi.org/10.1016/j.ijar.2020.05.008.

@article{43128,
   author = {Koczkodaj, W. W. and Liu, F. and Marek, J. and Mazurek, M. and Mazurek, Jiří and Mikhailov, L. and Özel, C. and Pedrycz, W. and Przelaskowski, A. and Schumann, A. and Smarzewski, R. and Strzalka, D. and Szybowski, J. and Yayli, Y.},
   article_location = {Amsterdam, Nizozemí},
   article_number = {124},
   doi = {http://dx.doi.org/10.1016/j.ijar.2020.05.008},
   keywords = {Pairwise comparisons; Inconsistency; Approximate reasoning; Group theory},
   language = {eng},
   issn = {0888-613X},
   journal = {International Journal of Approximate Reasoning},
   title = {On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note},
   url = {https://www.sciencedirect.com/science/article/pii/S0888613X2030178X},
   volume = {Neuveden},
   year = {2020}
}

TY  - JOUR
ID  - 43128
AU  - Koczkodaj, W. W. - Liu, F. - Marek, J. - Mazurek, M. - Mazurek, Jiří - Mikhailov, L. - Özel, C. - Pedrycz, W. - Przelaskowski, A. - Schumann, A. - Smarzewski, R. - Strzalka, D. - Szybowski, J. - Yayli, Y.
PY  - 2020
TI  - On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note
JF  - International Journal of Approximate Reasoning
VL  - Neuveden
IS  - 124
SP  - 59-65
EP  - 59-65
PB  - Elsevier
SN  - 0888613X
KW  - Pairwise comparisons
KW  - Inconsistency
KW  - Approximate reasoning
KW  - Group theory
UR  - https://www.sciencedirect.com/science/article/pii/S0888613X2030178X
L2  - https://www.sciencedirect.com/science/article/pii/S0888613X2030178X
N2  - 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.
ER  -

KOCZKODAJ, W. W., F. LIU, J. MAREK, M. MAZUREK, Jiří MAZUREK, L. MIKHAILOV, C. ÖZEL, W. PEDRYCZ, A. PRZELASKOWSKI, A. SCHUMANN, R. SMARZEWSKI, D. STRZALKA, J. SZYBOWSKI and Y. YAYLI. On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note. \textit{International Journal of Approximate Reasoning}. Amsterdam, Nizozemí: Elsevier, 2020, Neuveden, No~124, p.~59-65. ISSN~0888-613X. Available from: https://dx.doi.org/10.1016/j.ijar.2020.05.008.

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