Name
Title | ||
|---|---|---|
On the use of group theory to generalize elements of pairwise comparisons matrix: A cautionary note |
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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.ijar.2020.05.008 | International Journal of Approximate Reasoning |
Keywords | DocType | Volume |
Pairwise comparisons,Inconsistency,Approximate reasoning,Group theory | Journal | 124 |
Issue | ISSN | Citations |
1 | 0888-613X | 0 |
PageRank | References | Authors |
0.34 | 0 | 14 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Waldemar W. Koczkodaj | 1 | 628 | 100.50 |
| Fang Liu | 2 | 202 | 10.33 |
| V.W. Marek | 3 | 0 | 0.34 |
| J. Mazurek | 4 | 6 | 1.92 |
| Miroslaw Mazurek | 5 | 6 | 5.67 |
| Ludmil Mikhailov | 6 | 215 | 14.89 |
| C. Özel | 7 | 0 | 0.34 |
| W. Pedrycz | 8 | 13966 | 1005.85 |
| Artur Przelaskowski | 9 | 32 | 13.08 |
| Andrew Schumann | 10 | 104 | 20.44 |
| Ryszard Smarzewski | 11 | 9 | 5.47 |
| Dominik Strzałka | 12 | 18 | 5.42 |
| J. Szybowski | 13 | 43 | 8.45 |
| yusuf yayli | 14 | 1 | 0.96 |