2844. A geometric characterization of Pareto optimal weight vectors for 4x4 pairwise comparison matrices
Invited abstract in session WA-10: Pairwise comparisons and preference relations 2, stream Multiple Criteria Decision Aiding.
Wednesday, 8:30-10:00Room: Clarendon SR 1.06
Authors (first author is the speaker)
| 1. | Kristóf Ábele-Nagy
|
| Institute of Operations and Decision Sciences, Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest | |
| 2. | Sándor Bozóki
|
| Research Group of Operations Research and Decision Systems, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) | |
| 3. | Zsombor Szádoczki
|
| Research Laboratory on Engineering & Management Intelligence, HUN-REN Institute for Computer Science and Control (SZTAKI);, Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest |
Abstract
Pairwise comparison matrices, as Saaty proposed them half a century ago,
have become a central concept in preference modelling and decision
support.
A weight vector is called Pareto optimal (efficient) if no other weight
vector exists such that the ratios of its coordinates are at least as
close to the matrix elements, and at least one of them is strictly
closer. Despite the natural and simple definition, the geometric
characterization of Pareto optimal weight vectors has just begun. We
show that, if there is no consistent triad, then the set of normalized,
Pareto optimal weight vectors is the union of three tetrahedra, the
vertices of which correspond to weight vectors calculated from special
spanning trees, 4-paths. Each tetrahedron is associated to a
Hamiltonian cycle. If there are consistent triad(s) in the matrix, some
tetrahedra collapse to smaller dimensions. If the matrix itself is
consistent, all the three tetrahedra collapse to a single point.
Keywords
- Analytic Hierarchy Process
Status: accepted
Back to the list of papers