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A Qualitative Reasoning Approach to Measure Consensus

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Book cover Consensual Processes

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 267))

Abstract

This chapter introduces a mathematical framework on the basis of the absolute order-of-magnitude qualitative model. This framework allows to develop a methodology to assess the consensus found among different evaluators who use ordinal scales in group decision-making and evaluation processes. The concept of entropy is introduced in this context and the algebraic structure induced in the set of qualitative descriptions given by evaluators is studied. We prove that it is a weak partial semilattice structure that in some conditions takes the form of a distributive lattice. The definition of the entropy of a qualitatively-described system enables us, on one hand, to measure the amount of information provided by each evaluator and, on the other hand, to consider a degree of consensus among the evaluation committee. The methodology presented is able of managing situations where the assessment given by experts involves different levels of precision. In addition, when there is no consensus within the group decision, an automatic process measures the effort necessary to reach said consensus.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics 2, Universitat Politècnica de Catalunya, Barcelona, Spain

    Llorenç Roselló, Francesc Prats & Mónica Sánchez

  2. ESADE, Universitat Ramon Llull, Barcelona, Spain

    Núria Agell

Authors
  1. Llorenç Roselló
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  2. Francesc Prats
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  3. Núria Agell
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  4. Mónica Sánchez
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Editor information

Editors and Affiliations

  1. Depto. Ciencias de la Computación e Inteligencia Artificial, Universidad Granada, C/ Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Enrique Herrera-Viedma

  2. Departamento de Economía Aplicada, Universidad de Valladolid, Avenida Valle Esgueva 6, 47011, Valladolid, Spain

    José Luis García-Lapresta

  3. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

  4. Fac. Economia Dipto. Informatica e Studi Aziendali, Università di Trento, Via Inama 5, 38100, Trento, Trento, Italy

    Mario Fedrizzi

  5. Department of Political Science and Contemporary History, University of Turku, Turku, Finland

    Hannu Nurmi

  6. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Sławomir Zadrożny

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Roselló, L., Prats, F., Agell, N., Sánchez, M. (2011). A Qualitative Reasoning Approach to Measure Consensus. In: Herrera-Viedma, E., García-Lapresta, J.L., Kacprzyk, J., Fedrizzi, M., Nurmi, H., Zadrożny, S. (eds) Consensual Processes. Studies in Fuzziness and Soft Computing, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20533-0_14

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  • DOI: https://doi.org/10.1007/978-3-642-20533-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20532-3

  • Online ISBN: 978-3-642-20533-0

  • eBook Packages: EngineeringEngineering (R0)

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