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. |
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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, 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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