| 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, Neuveden, č. 124, s. 59-65. ISSN 0888-613X. doi:10.1016/j.ijar.2020.05.008. 2020. |
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@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, Neuveden, č.~124, s.~59-65. ISSN~0888-613X. doi:10.1016/j.ijar.2020.05.008. 2020.
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