70. A new nucleolus-like method to compute the priority vector of a pairwise comparison matrix
Invited abstract in session WC-2: Algorithms, stream Game theory.
Wednesday, 10:00 - 11:30Room: C 103
Authors (first author is the speaker)
| 1. | David Bartl
|
| Department of Informatics and Mathematics, Silesian University in Opava / School of Business Administration in Karviná |
Abstract
In multiple-criteria decision-making, given objects, such as alternatives, are often evaluated pairwise with respect to some criterion. The relative importance of the two elements in a pair is usually rated by a real number and by using the multiplicative scale; that is, the number means how many times an element is better (or more important) than the other in the pair. Then, the Geometric Mean Method (GMM) and Saaty’s Eigenvector Method (EVM) are prominently used to find the priority vector of a given pairwise comparison matrix (PCM).
In this paper, we consider the more general case when the entries of the PCM are elements of a divisible alo-group (Abelian linearly ordered group), cf. the “general unified framework for pairwise comparison matrices in multicriteria methods” by Cavallo & D’Apuzzo (2009). In this case, Saaty’s EVM cannot be used due to its intrinsic properties. The GMM can easily be adapted to find the priority vector of the PCM with entries from a divisible alo-group (Cavallo & D’Apuzzo, 2012) and, to our best knowledge, is the only currently known method that can be used in this setting.
Inspired by the concept of nucleolus from cooperative game theory (Schmeidler, 1969), we propose a new nucleolus-like method to compute the priority vector of a pairwise comparison matrix with entries from any divisible alo-group. The method utilizes the theory of linear programming in abstract spaces (Bartl, 2007).
Keywords
- Optimization under uncertainty and applications
Status: accepted
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