Incomplete Pairwise Comparison Matrices and Weighting Methods

László Csató, L. Rónyai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the linear order preservation property if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Original languageEnglish
Pages (from-to)309-320
Number of pages12
JournalFundamenta Informaticae
Volume144
Issue number3-4
DOIs
Publication statusPublished - May 2 2016

Fingerprint

Pairwise Comparisons
Eigenvalues and eigenfunctions
Weighting
Linear Order
Preservation
Eigenvector
Ranking
Partial Information
Directed Acyclic Graph
Axiom
Least Square Method
Logarithmic
Alternatives
Graph in graph theory

Keywords

  • Directed acyclic graph
  • EigenvectorMethod
  • incomplete pairwise comparison matrix
  • Logarithmic Least Squares Method

ASJC Scopus subject areas

  • Information Systems
  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Algebra and Number Theory

Cite this

Incomplete Pairwise Comparison Matrices and Weighting Methods. / Csató, László; Rónyai, L.

In: Fundamenta Informaticae, Vol. 144, No. 3-4, 02.05.2016, p. 309-320.

Research output: Contribution to journalArticle

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