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Distance–Based Characterization of Inconsistency in Pairwise Comparisons

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 300))

Abstract

This paper deals with the evaluation of preference consistency in decision making, assuming that decision makers express their preferences by means of pairwise comparisons in the set of alternatives. Preferences can be expressed using one of the various known representations, such as fuzzy preference relations or multiplicative pairwise comparison matrices. A geometrical characterization of inconsistency evaluation is proposed by considering a pairwise comparison matrix as a point in the vector space of square matrices of order n and by using different metrics to measure deviation of this matrix from full consistency. An inconsistency index is defined as the minimum distance of a pairwise comparison matrix from a consistent one, according to a fixed metric. Consequently, to each choice of a particular metric corresponds an inconsistency index. Geometrical properties of the subset of consistent matrices are investigated.

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Authors and Affiliations

  1. Department of Computer and Management Sciences, University of Trento, via Inama 5, 38122, Trento, Italy

    Michele Fedrizzi

Authors
  1. Michele Fedrizzi
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Fedrizzi, M. (2012). Distance–Based Characterization of Inconsistency in Pairwise Comparisons. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-31724-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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