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Consensus-Based Clustering in Numerical Decision-Making

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Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

In this paper, we consider that a set of agents assess a set of alternatives through numbers in the unit interval. In this setting, we introduce a measure that assigns a degree of consensus to each subset of agents with respect to every subset of alternatives. This consensus measure is defined as 1 minus the outcome generated by a symmetric aggregation function to the distances between the corresponding individual assessments. We establish some properties of the consensus measure, some of them depending on the used aggregation function. We also introduce an agglomerative hierarchical clustering procedure that is generated by similarity functions based on the previous consensus measures.

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Acknowledgments

The authors gratefully acknowledge the funding support of the Spanish Ministerio de Economía y Competitividad (project ECO2012-32178) and Consejería de Educación de la Junta de Castilla y León (project VA066U13).

Author information

Authors and Affiliations

  1. PRESAD Research Group, BORDA Research Unit, IMUVA, Dept. de Economía Aplicada, Universidad de Valladolid, Valladolid, Spain

    José Luis García-Lapresta

  2. PRESAD Research Group, BORDA Research Unit, Dep. de Organización de Empresas y C.I.M., Universidad de Valladolid, Valladolid, Spain

    David Pérez-Román

Authors
  1. José Luis García-Lapresta
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  2. David Pérez-Román
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Corresponding author

Correspondence to José Luis García-Lapresta .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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García-Lapresta, J.L., Pérez-Román, D. (2017). Consensus-Based Clustering in Numerical Decision-Making. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_30

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

  • eBook Packages: EngineeringEngineering (R0)

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