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.

Základní údaje

Originální název

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

Autoři

KOCZKODAJ, W. W. (124 Kanada, garant), F. LIU, J. MAREK (840 Spojené státy), M. MAZUREK (616 Polsko), Jiří MAZUREK (203 Česká republika, domácí), L. MIKHAILOV (826 Velká Británie a Severní Irsko), C. ÖZEL, W. PEDRYCZ (124 Kanada), A. PRZELASKOWSKI (616 Polsko), A. SCHUMANN (616 Polsko), R. SMARZEWSKI (616 Polsko), D. STRZALKA (616 Polsko), J. SZYBOWSKI (616 Polsko) a Y. YAYLI

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Kód RIV

RIV/47813059:19520/20:A0000117

Organizační jednotka

Obchodně podnikatelská fakulta v Karviné

DOI

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

UT WoS

000564641500004

Klíčová slova anglicky

Pairwise comparisons; Inconsistency; Approximate reasoning; Group theory

Příznaky

Mezinárodní význam, Recenzováno

Návaznosti

GA18-01246S, projekt VaV.

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

Anotace

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 a 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, č. 124, s. 59-65. ISSN 0888-613X. Dostupné z: 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 a 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, č.~124, s.~59-65. ISSN~0888-613X. Dostupné z: https://dx.doi.org/10.1016/j.ijar.2020.05.008.

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